2020 Publications

• Jakob Lemvig and Kamilla Haahr Nielsen (2020) Gabor windows supported on {1,1$} and construction of compactly supported dual windows with optimal smoothness. J. Approx. Theory, 249:105304. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig and Jordy Timo van Velthoven (2020) Criteria for generalized translation-invariant frames. Studia Math., 250(1):31–63. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

2019 Publications

• Enstad, Ulrik B. R., Mads S. Jakobsen and Luef, Franz (2019) Time-frequency analysis on the adeles over the rationals. C. R. Math. Acad. Sci. Paris, 357(2):188–199. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig and Kamilla Haahr Nielsen (2019) On the smoothness of dual windows for Gabor windows supported on {-1, 1$}. In Sampling Theory and Applications (SampTA), 2019 International Conference on. July http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads S. Jakobsen and Luef, Franz (2019) Sampling and periodization of generators of Heisenberg modules. Internat. J. Math., 30(10):1950051, 37. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Marzieh Hasannasab (2019) Gabor frames in \ell^2(\mathbb Z) and linear dependence. J. Fourier Anal. Appl., 25(1):101–107. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Marzieh Hasannasab (2019) Frame properties of systems arising via iterated actions of operators. Appl. Comput. Harmon. Anal., 46(3):664–673. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2019) The unitary extension principle on locally compact abelian groups. Appl. Comput. Harmon. Anal., 47(1):1–29. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

2018 Publications

• Hartmut Führ and Jakob Lemvig (2018) System bandwidth and the existence of generalized shift-invariant frames. J. Funct. Anal.. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads S. Jakobsen (2018) On a (no longer) new Segal algebra: a review of the Feichtinger algebra. J. Fourier Anal. Appl., 24(6):1579–1660. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2018) B-spline approximations of the Gaussian, their Gabor frame properties, and approximately dual frames. J. Fourier Anal. Appl., 24(4):1119–1140. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Janssen, Augustus J. E. M., Kim, Hong Oh and Kim, Rae Young (2018) Approximately dual Gabor frames and almost perfect reconstruction based on a class of window functions. Adv. Comput. Math., 44(5):1519–1535. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Marzieh Hasannasab (2018) Frames, operator representations, and open problems. In The diversity and beauty of applied operator theory, 155–165. . Birkhauser/Springer, Cham http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Marzieh Hasannasab and Diana T. Stoeva (2018) Operator representations of sequences and dynamical sampling. Sampl. Theory Signal Image Process., 17(1):29–42. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Marzieh Hasannasab and Ehsan Rashidi (2018) Dynamical sampling and frame representations with bounded operators. J. Math. Anal. Appl., 463(2):634–644. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

2017 Publications

• Ana Benavente, Ole Christensen and Maria I. Zakowicz (2017) Generalized shift-invariant systems and approximately dual frames. Ann. Funct. Anal., 8(2):177–189. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig (2017) On some Hermite series identities and their applications to Gabor analysis. Monatsh. Math., 182(4):899–912. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik and Jakob Lemvig (2017) Wavelets for non-expanding dilations and the lattice counting estimate. Int. Math. Res. Not. IMRN. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik, Mads S. Jakobsen, Jakob Lemvig and Kasso A. Okoudjou (2017) On Multivariate Wilson Bases. In Sampling Theory and Applications (SampTA), 2017 International Conference on. July http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik, Mads S. Jakobsen, Jakob Lemvig and Kasso A. Okoudjou (2017) On Wilson bases in L^2(\mathbb R^d). SIAM J. Math. Anal., 49(5):3999–4023. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2017) Differential equations and infinite series. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2017) Characterisations of partition of unities generated by entire functions in \mathbb C^d. Bull. Aust. Math. Soc., 95(2):281–290. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Marzieh Hasannasab (2017) Operator representations of frames: boundedness, duality, and stability. Integral Equations Operator Theory, 88(4):483–499. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Marzieh Hasannasab (2017) A characterization of tight and dual generalized translation invariant frames. In Sampling Theory and Applications (SampTA), 2017 International Conference on. July http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2017) Construction of Scaling Partitions of Unity. Frontiers in Applied Mathematics and Statistics, 3:21. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Marzieh Hasannasab, Jakob Lemvig (2017) Explicit constructions and properties of generalized shift-invariant systems in L^2(\mathbb R). Adv. Comput. Math., 43(2):443–472. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Peter Massopust, Birgitte Forster and Ole Christensen (2017) Fractional and complex pseudo-splines and the construction of Parseval frames. Appl. Math. Comput., 314:12–24. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

2016 Publications

• Diana T. Stoeva and Ole Christensen (2016) On various R-duals and the duality principle. Integral Equations Operator Theory, 84(4):577–590. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig and Kamilla Haahr Nielsen (2016) Counterexamples to the B-spline conjecture for Gabor frames. J. Fourier Anal. Appl., 22(6):1440–1451. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads Sielemann Jakobsen and Jakob Lemvig (2016) Reproducing formulas for generalized translation invariant systems on locally compact abelian groups. Trans. Amer. Math. Soc., 368(12):8447–8480. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads Sielemann Jakobsen and Jakob Lemvig (2016) Co-compact Gabor Systems on Locally Compact Abelian Groups. J. Fourier Anal. Appl., 22(1):36–70. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads Sielemann Jakobsen and Jakobsen Lemvig (2016) Density and duality theorems for regular Gabor frames. J. Funct. Anal., 270(1):229–263. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik and Jakob Lemvig (2016) Wavelets for non-expanding dilations and the lattice counting estimate. Int. Math. Res. Not.. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2016) On partition of unities generated by entire functions and Gabor frames in L^2(\mathbb R^d) and \ell^2(\mathbb Z^d). J. Fourier Anal. Appl., 22(5):1121–1140. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2016) On the Gabor frame set for compactly supported continuous functions. J. Inequal. Appl.. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

pub#2013?

.

#2014

#2015

#2014

#2013

• Diana T. Stoeva and Ole Christensen (2015) On R-duals and the duality principle in Gabor analysis. J. Fourier Anal. Appl., 21(2):383–400. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads Sielemann Jakobsen and Jakob Lemvig (2015) Duality results for co-compact Gabor systems. In Sampling Theory and Applications (SampTA), 2015 International Conference on. May, pages 144-147 http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads Sielemann Jakobsen and Jakob Lemvig (2015) A characterization of tight and dual generalized translation invariant frames. In Sampling Theory and Applications (SampTA), 2015 International Conference on. May, pages 96-100 http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Brigitte Forster and Peter Massopust (2015) Directional time--frequency analysis via continuous frames. Bull. Aust. Math. Soc., 92(2):268–281. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2015) On Gabor frames generated by sign-changing windows and B-splines. Appl. Comput. Harmon. Anal., 39(3):534–544. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2015) On entire functions restricted to intervals, partition of unities, and dual Gabor frames. Appl. Comput. Harmon. Anal., 38(1):72–86. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2015) Fourier-like frames on locally compact abelian groups. J. Approx. Theory, 192:82–101. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

• Mads Sielemann Jakobsen and Jakob Lemvig (2015) A characterization of tight and dual generalized translation invariant frames. In Sampling Theory and Applications (SampTA), 2015 International Conference on. May, pages 96-100 http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads Sielemann Jakobsen and Jakob Lemvig (2015) Duality results for co-compact Gabor systems. In Sampling Theory and Applications (SampTA), 2015 International Conference on. May, pages 144-147 http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2015) On Gabor frames generated by sign-changing windows and B-splines. Appl. Comput. Harmon. Anal., 39(3):534–544. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Brigitte Forster and Peter Massopust (2015) Directional time--frequency analysis via continuous frames. Bull. Aust. Math. Soc., 92(2):268–281. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Diana T. Stoeva and Ole Christensen (2015) On R-duals and the duality principle in Gabor analysis. J. Fourier Anal. Appl., 21(2):383–400. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2015) Fourier-like frames on locally compact abelian groups. J. Approx. Theory, 192:82–101. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2015) On entire functions restricted to intervals, partition of unities, and dual Gabor frames. Appl. Comput. Harmon. Anal., 38(1):72–86. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

• Ole Christensen, Marzieh Hasannasab and Friedrich Philipp (2018) Frame properties of operator orbits. (preprint). http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

• Ole Christensen and Say Song Goh (2015) Fourier-like frames on locally compact abelian groups. J. Approx. Theory, 192:82–101. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2015) On entire functions restricted to intervals, partition of unities, and dual Gabor frames. Appl. Comput. Harmon. Anal., 38(1):72–86. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Diana T. Stoeva and Ole Christensen (2015) On R-duals and the duality principle in Gabor analysis. J. Fourier Anal. Appl., 21(2):383–400. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Brigitte Forster and Peter Massopust (2015) Directional time--frequency analysis via continuous frames. Bull. Aust. Math. Soc., 92(2):268–281. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads Sielemann Jakobsen and Jakob Lemvig (2015) Duality results for co-compact Gabor systems. In Sampling Theory and Applications (SampTA), 2015 International Conference on. May, pages 144-147 http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2015) On Gabor frames generated by sign-changing windows and B-splines. Appl. Comput. Harmon. Anal., 39(3):534–544. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads Sielemann Jakobsen and Jakob Lemvig (2015) A characterization of tight and dual generalized translation invariant frames. In Sampling Theory and Applications (SampTA), 2015 International Conference on. May, pages 96-100 http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

2014 Publications

2013 Publications

• Ole Christensen, Marzieh Hasannasab and Friedrich Philipp (2018) Frame properties of operator orbits. (preprint). http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

Preprints

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2015 Publications

2013 & 2014 Publications

• Click https://hata.compute.dtu.dk/pub/../files/world.png to go to the arXiv or, if available, the journal version of the paper (DOI links)

comment * Click https://hata.compute.dtu.dk/pub/../files/pdf.png to obtain preprint versions.

Preprints & 2015 Publications

• Mads Sielemann Jakobsen and Jakob Lemvig (2015) A characterization of tight and dual generalized translation invariant frames. In Sampling Theory and Applications (SampTA), 2015 International Conference on. May, pages 96-100 http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2015) On Gabor frames generated by sign-changing windows and B-splines. Appl. Comput. Harmon. Anal., 39(3):534–544. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads Sielemann Jakobsen and Jakob Lemvig (2015) Duality results for co-compact Gabor systems. In Sampling Theory and Applications (SampTA), 2015 International Conference on. May, pages 144-147 http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Brigitte Forster and Peter Massopust (2015) Directional time--frequency analysis via continuous frames. Bull. Aust. Math. Soc., 92(2):268–281. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Diana T. Stoeva and Ole Christensen (2015) On R-duals and the duality principle in Gabor analysis. J. Fourier Anal. Appl., 21(2):383–400. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2015) On entire functions restricted to intervals, partition of unities, and dual Gabor frames. Appl. Comput. Harmon. Anal., 38(1):72–86. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2015) Fourier-like frames on locally compact abelian groups. J. Approx. Theory, 192:82–101. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

2007 - 2014 Publications

• Felix Krahmer, Gitta Kutyniok and Jakob Lemvig (2014) Sparse matrices in frame theory. Comput. Statist., 29(3-4):547–568. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig, Christopher Miller and Kasso A. Okoudjou (2014) Prime tight frames. Adv. Comput. Math., 40(2):315–334. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2014) Frames and extension problems I. In Fractals, wavelets, and their applications, 219–234. . Springer, Cham http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2014) Six (seven) problems in frame theory. In New perspectives on approximation and sampling theory, 337–358. . Birkhauser/Springer, Cham http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2014) A short introduction to frames, Gabor systems, and wavelet systems. Azerb. J. Math., 4(1):25–39. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2014) Frames and extension problems II. In Fractals, wavelets, and their applications, 235–243. . Springer, Cham http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2014) On Parseval wavelet frames with two or three generators via the unitary extension principle. Canad. Math. Bull., 57(2):254–263. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2014) From dual pairs of Gabor frames to dual pairs of wavelet frames and vice versa. Appl. Comput. Harmon. Anal., 36(2):198–214. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

Preprints & 2014 Publications

• Felix Krahmer, Gitta Kutyniok and Jakob Lemvig (2014) Sparse matrices in frame theory. Comput. Statist., 29(3-4):547–568. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2014) Six (seven) problems in frame theory. In New perspectives on approximation and sampling theory, 337–358. . Birkhauser/Springer, Cham http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig, Christopher Miller and Kasso A. Okoudjou (2014) Prime tight frames. Adv. Comput. Math., 40(2):315–334. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2014) Frames and extension problems II. In Fractals, wavelets, and their applications, 235–243. . Springer, Cham http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2014) Frames and extension problems I. In Fractals, wavelets, and their applications, 219–234. . Springer, Cham http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2014) From dual pairs of Gabor frames to dual pairs of wavelet frames and vice versa. Appl. Comput. Harmon. Anal., 36(2):198–214. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2014) A short introduction to frames, Gabor systems, and wavelet systems. Azerb. J. Math., 4(1):25–39. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2014) On Parseval wavelet frames with two or three generators via the unitary extension principle. Canad. Math. Bull., 57(2):254–263. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

2007 - 2013 Publications

• Felix Krahmer, Gitta Kutyniok and Jakob Lemvig (2013) Sparsity and spectral properties of dual frames. Linear Algebra Appl., 439(4):982–998. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Lasse Hjuler Christiansen and Ole Christensen (2013) Construction of smooth compactly supported windows generating dual pairs of Gabor frames. Asian-Eur. J. Math., 6(1):1350011, 13. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Elnaz Osgooei (2013) On frame properties for Fourier-like systems. J. Approx. Theory, 172:47–57. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2013) Regularity of dual Gabor windows. Abstr. Appl. Anal.. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2013) Extensions of Bessel sequences to dual pairs of frames. Appl. Comput. Harmon. Anal., 34(2):224–233. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Xiang Chun Xiao and Yu Can Zhu (2013) Characterizing R-duality in Banach spaces. Acta Math. Sin. (Engl. Ser.), 29(1):75–84. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

Preprints & 2013 Publications

• Felix Krahmer, Gitta Kutyniok and Jakob Lemvig (2013) Sparsity and spectral properties of dual frames. Linear Algebra Appl., 439(4):982–998. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2013) Regularity of dual Gabor windows. Abstr. Appl. Anal.. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Elnaz Osgooei (2013) On frame properties for Fourier-like systems. J. Approx. Theory, 172:47–57. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Lasse Hjuler Christiansen and Ole Christensen (2013) Construction of smooth compactly supported windows generating dual pairs of Gabor frames. Asian-Eur. J. Math., 6(1):1350011, 13. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Xiang Chun Xiao and Yu Can Zhu (2013) Characterizing R-duality in Banach spaces. Acta Math. Sin. (Engl. Ser.), 29(1):75–84. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2013) Extensions of Bessel sequences to dual pairs of frames. Appl. Comput. Harmon. Anal., 34(2):224–233. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

2007 - 2012 Publications

• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Optimally sparse approximations of 3D functions by compactly supported shearlet frames. SIAM J. Math. Anal., 44(4):2962–3017. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Shearlets and Optimally Sparse Approximations. In Shearlets: Multiscale Analysis for Multivariate Data. (D. Labate and G. Kutyniok, Eds.), Springer. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Compactly supported shearlets. In Approximation Theory XIII: San Antonio 2010.. Springer Proc. Math., 163–186 (13). http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig (2012) Constructing pairs of dual bandlimited frame wavelets in L^2(R^n). Appl. Comput. Harmon. Anal., 32:313–328. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik, Ole Christensen, Xinli Huang and Baiyun Yu (2012) Extension of shift-invariant systems in L^2(R) to frames. Numer. Funct. Anal. Optim., 33(7-9):833–846. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Matcin Bownik and Jakob Lemvig (2012) Oversampling of wavelet frames for real dilations. Jour. London Math. Soc., 85:765–788. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Alex, er M. Powell and Xiang Chun Xiao (2012) A note on finite dual frame pairs. Proc. Amer. Math. Soc., 140(11):3921–3930. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2012) Gabor windows supported on [-1,1] and dual windows with small support. Adv. Comput. Math., 36(4):525–545. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Kristian Berg Thomsen and Mads Paulsen (2012) Gibbs phenomenon swinger in 2D. Normat, 60(1):15–30, 48 (2013). http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Peter Massopust (2012) Exponential B-splines and the partition of unity property. Adv. Comput. Math., 37(3):301–318. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2012) Pairs of dual periodic frames. Appl. Comput. Harmon. Anal., 33(3):315–329. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Optimally sparse approximations of 3D functions by compactly supported shearlet frames. SIAM J. Math. Anal., 44(4):2962–3017. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Shearlets and Optimally Sparse Approximations. In Shearlets: Multiscale Analysis for Multivariate Data. (D. Labate and G. Kutyniok, Eds.), Springer. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Compactly supported shearlets. In Approximation Theory XIII: San Antonio 2010.. Springer Proc. Math., 163–186 (13). http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig (2012) Constructing pairs of dual bandlimited frame wavelets in L^2(R^n). Appl. Comput. Harmon. Anal., 32:313–328. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik, Ole Christensen, Xinli Huang and Baiyun Yu (2012) Extension of shift-invariant systems in L^2(R) to frames. Numer. Funct. Anal. Optim., 33(7-9):833–846. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Matcin Bownik and Jakob Lemvig (2012) Oversampling of wavelet frames for real dilations. Jour. London Math. Soc., 85:765–788. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Alex, er M. Powell and Xiang Chun Xiao (2012) A note on finite dual frame pairs. Proc. Amer. Math. Soc., 140(11):3921–3930. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2012) Gabor windows supported on [-1,1] and dual windows with small support. Adv. Comput. Math., 36(4):525–545. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Kristian Berg Thomsen and Mads Paulsen (2012) Gibbs phenomenon swinger in 2D. Normat, 60(1):15–30, 48 (2013). http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Peter Massopust (2012) Exponential B-splines and the partition of unity property. Adv. Comput. Math., 37(3):301–318. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2012) Pairs of dual periodic frames. Appl. Comput. Harmon. Anal., 33(3):315–329. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Optimally sparse approximations of 3D functions by compactly supported shearlet frames. SIAM J. Math. Anal., 44(4):2962–3017. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Shearlets and Optimally Sparse Approximations. In Shearlets: Multiscale Analysis for Multivariate Data. (D. Labate and G. Kutyniok, Eds.), Springer. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Compactly supported shearlets. In Approximation Theory XIII: San Antonio 2010.. Springer Proc. Math., 163–186 (13). http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig (2012) Constructing pairs of dual bandlimited frame wavelets in L^2(R^n). Appl. Comput. Harmon. Anal., 32:313–328. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik, Ole Christensen, Xinli Huang and Baiyun Yu (2012) Extension of shift-invariant systems in L^2(R) to frames. Numer. Funct. Anal. Optim., 33(7-9):833–846. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Matcin Bownik and Jakob Lemvig (2012) Oversampling of wavelet frames for real dilations. Jour. London Math. Soc., 85:765–788. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Alex, er M. Powell and Xiang Chun Xiao (2012) A note on finite dual frame pairs. Proc. Amer. Math. Soc., 140(11):3921–3930. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2012) Gabor windows supported on [-1,1] and dual windows with small support. Adv. Comput. Math., 36(4):525–545. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Kristian Berg Thomsen and Mads Paulsen (2012) Gibbs phenomenon swinger in 2D. Normat, 60(1):15–30, 48 (2013). http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Peter Massopust (2012) Exponential B-splines and the partition of unity property. Adv. Comput. Math., 37(3):301–318. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2012) Pairs of dual periodic frames. Appl. Comput. Harmon. Anal., 33(3):315–329. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

Title: Wavelet Frames and Their Duals (pdf Δ). Supervisor: Ole Christensen. Thesis examiners: Prof. Per Christian Hansen (chairman, DTU), Prof. Say Song Goh (National University of Singapore), Prof. Richard S. Laugesen (University of Illinois, U.S.A.). Thesis defence: Friday September 26, 2008.

early?

• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Optimally sparse approximations of 3D functions by compactly supported shearlet frames. SIAM J. Math. Anal., 44(4):2962–3017. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Compactly supported shearlets. In Approximation Theory XIII: San Antonio 2010.. Springer Proc. Math., 163–186 (13). http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig (2012) Constructing pairs of dual bandlimited frame wavelets in L^2(R^n). Appl. Comput. Harmon. Anal., 32:313–328. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Matcin Bownik and Jakob Lemvig (2012) Oversampling of wavelet frames for real dilations. Jour. London Math. Soc., 85:765–788. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Shearlets and Optimally Sparse Approximations. In Shearlets: Multiscale Analysis for Multivariate Data. (D. Labate and G. Kutyniok, Eds.), Springer. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Kristian Berg Thomsen and Mads Paulsen (2012) Gibbs phenomenon swinger in 2D. Normat, 60(1):15–30, 48 (2013). http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Peter Massopust (2012) Exponential B-splines and the partition of unity property. Adv. Comput. Math., 37(3):301–318. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2012) Gabor windows supported on [-1,1] and dual windows with small support. Adv. Comput. Math., 36(4):525–545. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Alex, er M. Powell and Xiang Chun Xiao (2012) A note on finite dual frame pairs. Proc. Amer. Math. Soc., 140(11):3921–3930. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2012) Pairs of dual periodic frames. Appl. Comput. Harmon. Anal., 33(3):315–329. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik, Ole Christensen, Xinli Huang and Baiyun Yu (2012) Extension of shift-invariant systems in L^2(R) to frames. Numer. Funct. Anal. Optim., 33(7-9):833–846. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

• Marcin Bownik, Ole Christensen, Xinli Huang and Baiyun Yu (2012) Extension of shift-invariant systems in L^2(R) to frames. Numer. Funct. Anal. Optim., 33(7-9):833–846. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2012) Pairs of dual periodic frames. Appl. Comput. Harmon. Anal., 33(3):315–329. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Alex, er M. Powell and Xiang Chun Xiao (2012) A note on finite dual frame pairs. Proc. Amer. Math. Soc., 140(11):3921–3930. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2012) Gabor windows supported on [-1,1] and dual windows with small support. Adv. Comput. Math., 36(4):525–545. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Peter Massopust (2012) Exponential B-splines and the partition of unity property. Adv. Comput. Math., 37(3):301–318. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Kristian Berg Thomsen and Mads Paulsen (2012) Gibbs phenomenon swinger in 2D. Normat, 60(1):15–30, 48 (2013). http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Shearlets and Optimally Sparse Approximations. In Shearlets: Multiscale Analysis for Multivariate Data. (D. Labate and G. Kutyniok, Eds.), Springer. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Matcin Bownik and Jakob Lemvig (2012) Oversampling of wavelet frames for real dilations. Jour. London Math. Soc., 85:765–788. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig (2012) Constructing pairs of dual bandlimited frame wavelets in L^2(R^n). Appl. Comput. Harmon. Anal., 32:313–328. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Compactly supported shearlets. In Approximation Theory XIII: San Antonio 2010.. Springer Proc. Math., 163–186 (13). http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Optimally sparse approximations of 3D functions by compactly supported shearlet frames. SIAM J. Math. Anal., 44(4):2962–3017. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

• Marcin Bownik, Ole Christensen, Xinli Huang and Baiyun Yu (2012) Extension of shift-invariant systems in L^2(R) to frames. Numer. Funct. Anal. Optim., 33(7-9):833–846. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2012) Pairs of dual periodic frames. Appl. Comput. Harmon. Anal., 33(3):315–329. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Alex, er M. Powell and Xiang Chun Xiao (2012) A note on finite dual frame pairs. Proc. Amer. Math. Soc., 140(11):3921–3930. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2012) Gabor windows supported on [-1,1] and dual windows with small support. Adv. Comput. Math., 36(4):525–545. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Peter Massopust (2012) Exponential B-splines and the partition of unity property. Adv. Comput. Math., 37(3):301–318. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Kristian Berg Thomsen and Mads Paulsen (2012) Gibbs phenomenon swinger in 2D. Normat, 60(1):15–30, 48 (2013). http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Shearlets and Optimally Sparse Approximations. In Shearlets: Multiscale Analysis for Multivariate Data. (D. Labate and G. Kutyniok, Eds.), Springer. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Matcin Bownik and Jakob Lemvig (2012) Oversampling of wavelet frames for real dilations. Jour. London Math. Soc., 85:765–788. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig (2012) Constructing pairs of dual bandlimited frame wavelets in L^2(R^n). Appl. Comput. Harmon. Anal., 32:313–328. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Compactly supported shearlets. In Approximation Theory XIII: San Antonio 2010.. Springer Proc. Math., 163–186 (13). http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Optimally sparse approximations of 3D functions by compactly supported shearlet frames. SIAM J. Math. Anal., 44(4):2962–3017. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

Title: Wavelet Frames and Their Duals (pdf Δ). Supervisor: Ole Christensen. Thesis examiners: Prof. Per Christian Hansen (chairman, DTU), Prof. Say Song Goh (National University of Singapore), Prof. Richard S. Laugesen (University of Illinois, U.S.A.). Thesis defence: Friday September 26, 2008.

2007 - 2011 Publications

• Marcin Bownik and Jakob Lemvig (2007) The canonical and alternate duals of a wavelet frame. Appl. Comput. Harmon. Anal., 23(2):263–272. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik and Ole Christensen (2007) Characterization and perturbation of Gabor frame sequences with rational parameters. J. Approx. Theory, 147(1):67–80. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

• Ole Christensen (2008) Frames and bases. Birkhauser Boston, Inc., Boston, MA http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Asghar Rahimi (2008) Frame properties of wave packet systems in L^2(R^d). Adv. Comput. Math., 29(2):101–111. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Wenchang Sun (2008) Explicitly given pairs of dual frames with compactly supported generators and applications to irregular B-splines. J. Approx. Theory, 151(2):155–163. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Peter G. Casazza and Ole Christensen (2008) The reconstruction property in Banach spaces and a perturbation theorem. Canad. Math. Bull., 51(3):348–358. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

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Ph.D. Thesis

Title: Wavelet Frames and Their Duals (pdf Δ). Supervisor: Ole Christensen. Thesis examiners: Prof. Per Christian Hansen (chairman, DTU), Prof. Say Song Goh (National University of Singapore), Prof. Richard S. Laugesen (University of Illinois, U.S.A.). Thesis defence: Friday September 26, 2008.

• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2011) Optimally sparse approximations of multivariate functions using compactly supported shearlet frames. SampTA'11 (Singapore, 2011) Proc. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Matcin Bownik and Jakob Lemvig (2011) Affine and quasi-affine frames for rational dilations. Trans. Amer. Math. Soc., 363(4):1887–1924. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2011) On the duality principle by Casazza, Kutyniok, and Lammers. J. Fourier Anal. Appl., 17(4):640–655. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Mads Sielemann Jakobsen (2011) Dual pairs of Gabor frames for trigonometric generators without the partition of unity property. Asian-Eur. J. Math., 4(4):589–603. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Mads Sielemann Jakobsen (2011) Series representations in L^2(R) of products of trigonometric functions. Normat, 59(1):22–43, 48. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2010) Functions, spaces, and expansions. Birkhauser Boston, Inc., Boston, MA http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2010) Gabor windows supported on [-1,1] and compactly supported dual windows. Appl. Comput. Harmon. Anal., 28(1):89–103. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Rae Young Kim (2010) On dual Gabor frame pairs generated by polynomials. J. Fourier Anal. Appl., 16(1):1–16. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Richard S. Laugesen (2010) Approximately dual frames in Hilbert spaces and applications to Gabor frames. Sampl. Theory Signal Image Process., 9(1-3):77–89. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2010) Pairs of oblique duals in spaces of periodic functions. Adv. Comput. Math., 32(3):353–379. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig (2009) Constructing pairs of dual bandlimited framelets with desired time localization. Adv. Comput. Math., 30(3):231–247. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Hartmut Führ and Jakob Lemvig (2018) System bandwidth and the existence of generalized shift-invariant frames. J. Funct. Anal.. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads S. Jakobsen (2018) On a (no longer) new Segal algebra: a review of the Feichtinger algebra. J. Fourier Anal. Appl., 24(6):1579–1660. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2018) B-spline approximations of the Gaussian, their Gabor frame properties, and approximately dual frames. J. Fourier Anal. Appl., 24(4):1119–1140. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Janssen, Augustus J. E. M., Kim, Hong Oh and Kim, Rae Young (2018) Approximately dual Gabor frames and almost perfect reconstruction based on a class of window functions. Adv. Comput. Math., 44(5):1519–1535. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Marzieh Hasannasab (2018) Frames, operator representations, and open problems. In The diversity and beauty of applied operator theory, 155–165. . Birkhauser/Springer, Cham http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Marzieh Hasannasab and Diana T. Stoeva (2018) Operator representations of sequences and dynamical sampling. Sampl. Theory Signal Image Process., 17(1):29–42. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Marzieh Hasannasab and Ehsan Rashidi (2018) Dynamical sampling and frame representations with bounded operators. J. Math. Anal. Appl., 463(2):634–644. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Marzieh Hasannasab and Friedrich Philipp (2018) Frame properties of operator orbits. (preprint). http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

Abstract. Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame is a frame-like collection of subspaces in a Hilbert space, thereby generalizing the concept of a frame for signal representation. In this paper, we study the existence and construction of fusion frames. We first present a complete characterization of a special class of fusion frames, called Parseval fusion frames. The value of Parseval fusion frames is that the inverse fusion frame operator is equal to the identity and therefore signal reconstruction can be performed with minimal complexity. We then introduce two general methods $ndash; the spatial complement and the Naimark complement - for constructing a new fusion frame from a given fusion frame. We then establish existence conditions for fusion frames with desired properties. In particular, we address the following question: Given M, N, m \in \mathbb{N} and \{\lambda_j\}_{j=1,...,M}, does there exist a fusion frame in \mathbb{R}^M with N subspaces of dimension m for which \{\lambda_j\}_{j=1,...,M} are the eigenvalues of the associated fusion frame operator? We address this problem by providing an algorithm which computes such a fusion frame for almost any collection of parameters M, N, m \in \mathbb{N} and \{\lambda_j\}_{j=1,...,M}. Moreover, we show how this procedure can be applied, if subspaces are to be added to a given fusion frame to force it to become Parseval.

Publications

Preprints

Preprints & 2012 Publications

• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Optimally sparse approximations of 3D functions by compactly supported shearlet frames. SIAM J. Math. Anal., 44(4):2962–3017. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Shearlets and Optimally Sparse Approximations. In Shearlets: Multiscale Analysis for Multivariate Data. (D. Labate and G. Kutyniok, Eds.), Springer. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Compactly supported shearlets. In Approximation Theory XIII: San Antonio 2010.. Springer Proc. Math., 163–186 (13). http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig (2012) Constructing pairs of dual bandlimited frame wavelets in L^2(R^n). Appl. Comput. Harmon. Anal., 32:313–328. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik, Ole Christensen, Xinli Huang and Baiyun Yu (2012) Extension of shift-invariant systems in L^2(R) to frames. Numer. Funct. Anal. Optim., 33(7-9):833–846. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Matcin Bownik and Jakob Lemvig (2012) Oversampling of wavelet frames for real dilations. Jour. London Math. Soc., 85:765–788. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Alex, er M. Powell and Xiang Chun Xiao (2012) A note on finite dual frame pairs. Proc. Amer. Math. Soc., 140(11):3921–3930. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2012) Gabor windows supported on [-1,1] and dual windows with small support. Adv. Comput. Math., 36(4):525–545. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Kristian Berg Thomsen and Mads Paulsen (2012) Gibbs phenomenon swinger in 2D. Normat, 60(1):15–30, 48 (2013). http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Peter Massopust (2012) Exponential B-splines and the partition of unity property. Adv. Comput. Math., 37(3):301–318. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2012) Pairs of dual periodic frames. Appl. Comput. Harmon. Anal., 33(3):315–329. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

2008 - 2011 Publications

Quick Guide:

• Jakob Lemvig and Jordy Timo van Velthoven (2020) Criteria for generalized translation-invariant frames. Studia Math., 250(1):31–63. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig and Kamilla Haahr Nielsen (2020) Gabor windows supported on {1,1$} and construction of compactly supported dual windows with optimal smoothness. J. Approx. Theory, 249:105304. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Marzieh Hasannasab (2019) Gabor frames in \ell^2(\mathbb Z) and linear dependence. J. Fourier Anal. Appl., 25(1):101–107. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig and Kamilla Haahr Nielsen (2019) On the smoothness of dual windows for Gabor windows supported on {-1, 1$}. In Sampling Theory and Applications (SampTA), 2019 International Conference on. July http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Marzieh Hasannasab (2019) Frame properties of systems arising via iterated actions of operators. Appl. Comput. Harmon. Anal., 46(3):664–673. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2019) The unitary extension principle on locally compact abelian groups. Appl. Comput. Harmon. Anal., 47(1):1–29. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads S. Jakobsen and Luef, Franz (2019) Sampling and periodization of generators of Heisenberg modules. Internat. J. Math., 30(10):1950051, 37. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Enstad, Ulrik B. R., Mads S. Jakobsen and Luef, Franz (2019) Time-frequency analysis on the adeles over the rationals. C. R. Math. Acad. Sci. Paris, 357(2):188–199. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Marzieh Hasannasab and Ehsan Rashidi (2018) Dynamical sampling and frame representations with bounded operators. J. Math. Anal. Appl., 463(2):634–644. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Marzieh Hasannasab (2018) Frames, operator representations, and open problems. In The diversity and beauty of applied operator theory, 155–165. . Birkhauser/Springer, Cham http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Marzieh Hasannasab and Friedrich Philipp (2018) Frame properties of operator orbits. (preprint). http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Marzieh Hasannasab and Diana T. Stoeva (2018) Operator representations of sequences and dynamical sampling. Sampl. Theory Signal Image Process., 17(1):29–42. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Hartmut Führ and Jakob Lemvig (2018) System bandwidth and the existence of generalized shift-invariant frames. J. Funct. Anal.. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Janssen, Augustus J. E. M., Kim, Hong Oh and Kim, Rae Young (2018) Approximately dual Gabor frames and almost perfect reconstruction based on a class of window functions. Adv. Comput. Math., 44(5):1519–1535. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads S. Jakobsen (2018) On a (no longer) new Segal algebra: a review of the Feichtinger algebra. J. Fourier Anal. Appl., 24(6):1579–1660. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2018) B-spline approximations of the Gaussian, their Gabor frame properties, and approximately dual frames. J. Fourier Anal. Appl., 24(4):1119–1140. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Marzieh Hasannasab (2017) Operator representations of frames: boundedness, duality, and stability. Integral Equations Operator Theory, 88(4):483–499. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2017) Characterisations of partition of unities generated by entire functions in \mathbb C^d. Bull. Aust. Math. Soc., 95(2):281–290. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ana Benavente, Ole Christensen and Maria I. Zakowicz (2017) Generalized shift-invariant systems and approximately dual frames. Ann. Funct. Anal., 8(2):177–189. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Peter Massopust, Birgitte Forster and Ole Christensen (2017) Fractional and complex pseudo-splines and the construction of Parseval frames. Appl. Math. Comput., 314:12–24. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik, Mads S. Jakobsen, Jakob Lemvig and Kasso A. Okoudjou (2017) On Wilson bases in L^2(\mathbb R^d). SIAM J. Math. Anal., 49(5):3999–4023. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2017) Construction of Scaling Partitions of Unity. Frontiers in Applied Mathematics and Statistics, 3:21. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Marzieh Hasannasab (2017) A characterization of tight and dual generalized translation invariant frames. In Sampling Theory and Applications (SampTA), 2017 International Conference on. July http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik and Jakob Lemvig (2017) Wavelets for non-expanding dilations and the lattice counting estimate. Int. Math. Res. Not. IMRN. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig (2017) On some Hermite series identities and their applications to Gabor analysis. Monatsh. Math., 182(4):899–912. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Marzieh Hasannasab, Jakob Lemvig (2017) Explicit constructions and properties of generalized shift-invariant systems in L^2(\mathbb R). Adv. Comput. Math., 43(2):443–472. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik, Mads S. Jakobsen, Jakob Lemvig and Kasso A. Okoudjou (2017) On Multivariate Wilson Bases. In Sampling Theory and Applications (SampTA), 2017 International Conference on. July http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2017) Differential equations and infinite series. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2016) On the Gabor frame set for compactly supported continuous functions. J. Inequal. Appl.. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2016) On partition of unities generated by entire functions and Gabor frames in L^2(\mathbb R^d) and \ell^2(\mathbb Z^d). J. Fourier Anal. Appl., 22(5):1121–1140. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Diana T. Stoeva and Ole Christensen (2016) On various R-duals and the duality principle. Integral Equations Operator Theory, 84(4):577–590. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads Sielemann Jakobsen and Jakob Lemvig (2016) Co-compact Gabor Systems on Locally Compact Abelian Groups. J. Fourier Anal. Appl., 22(1):36–70. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads Sielemann Jakobsen and Jakobsen Lemvig (2016) Density and duality theorems for regular Gabor frames. J. Funct. Anal., 270(1):229–263. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads Sielemann Jakobsen and Jakob Lemvig (2016) Reproducing formulas for generalized translation invariant systems on locally compact abelian groups. Trans. Amer. Math. Soc., 368(12):8447–8480. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik and Jakob Lemvig (2016) Wavelets for non-expanding dilations and the lattice counting estimate. Int. Math. Res. Not.. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig and Kamilla Haahr Nielsen (2016) Counterexamples to the B-spline conjecture for Gabor frames. J. Fourier Anal. Appl., 22(6):1440–1451. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2015) Fourier-like frames on locally compact abelian groups. J. Approx. Theory, 192:82–101. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2015) On Gabor frames generated by sign-changing windows and B-splines. Appl. Comput. Harmon. Anal., 39(3):534–544. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Diana T. Stoeva and Ole Christensen (2015) On R-duals and the duality principle in Gabor analysis. J. Fourier Anal. Appl., 21(2):383–400. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Brigitte Forster and Peter Massopust (2015) Directional time--frequency analysis via continuous frames. Bull. Aust. Math. Soc., 92(2):268–281. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2015) On entire functions restricted to intervals, partition of unities, and dual Gabor frames. Appl. Comput. Harmon. Anal., 38(1):72–86. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads Sielemann Jakobsen and Jakob Lemvig (2015) A characterization of tight and dual generalized translation invariant frames. In Sampling Theory and Applications (SampTA), 2015 International Conference on. May, pages 96-100 http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads Sielemann Jakobsen and Jakob Lemvig (2015) Duality results for co-compact Gabor systems. In Sampling Theory and Applications (SampTA), 2015 International Conference on. May, pages 144-147 http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig, Christopher Miller and Kasso A. Okoudjou (2014) Prime tight frames. Adv. Comput. Math., 40(2):315–334. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2014) Six (seven) problems in frame theory. In New perspectives on approximation and sampling theory, 337–358. . Birkhauser/Springer, Cham http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Felix Krahmer, Gitta Kutyniok and Jakob Lemvig (2014) Sparse matrices in frame theory. Comput. Statist., 29(3-4):547–568. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2014) Frames and extension problems II. In Fractals, wavelets, and their applications, 235–243. . Springer, Cham http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2014) From dual pairs of Gabor frames to dual pairs of wavelet frames and vice versa. Appl. Comput. Harmon. Anal., 36(2):198–214. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2014) Frames and extension problems I. In Fractals, wavelets, and their applications, 219–234. . Springer, Cham http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2014) On Parseval wavelet frames with two or three generators via the unitary extension principle. Canad. Math. Bull., 57(2):254–263. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

• Ole Christensen and Yonina C. Eldar (2005) Generalized shift-invariant systems and frames for subspaces. J. Fourier Anal. Appl., 11(3):299–313. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Khadija L. Christensen (2005) Approximation theory. Birkhauser Boston, Inc., Boston, MA http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, H. O. Kim, R. Y. Kim and J. K. Lim (2005) Perturbation of frame sequences in shift-invariant spaces. J. Geom. Anal., 15(2):181–192. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Peter G. Casazza, Ole Christensen, Shidong Li, Alex and er Lindner (2006) Density results for frames of exponentials. In Harmonic analysis and applications, 359–369. . Birkhauser Boston, Boston, MA http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Yonina C. Eldar and Ole Christensen (2006) Characterization of oblique dual frame pairs. EURASIP J. Appl. Signal Process.. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, H. O. Kim, R. Y. Kim and J. K. Lim (2006) Riesz sequences of translates and generalized duals with support on {0,1$}. J. Geom. Anal., 16(4):585–596. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Khadija L. Christensen (2006) Linear independence and series expansions in function spaces. Amer. Math. Monthly, 113(7):611–627. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2006) Frames and generalized shift-invariant systems. In Pseudo-differential operators and related topics, 193–209. . Birkhauser, Basel http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2006) Pairs of dual Gabor frame generators with compact support and desired frequency localization. Appl. Comput. Harmon. Anal., 20(3):403–410. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Wenchang Sun (2006) Stability of wavelet frames with matrix dilations. Proc. Amer. Math. Soc., 134(3):831–842 (electronic). http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Rae Young Kim (2006) Pairs of explicitly given dual Gabor frames in L^2(R^d). J. Fourier Anal. Appl., 12(3):243–255. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik and Jakob Lemvig (2007) The canonical and alternate duals of a wavelet frame. Appl. Comput. Harmon. Anal., 23(2):263–272. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik and Ole Christensen (2007) Characterization and perturbation of Gabor frame sequences with rational parameters. J. Approx. Theory, 147(1):67–80. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Peter G. Casazza and Ole Christensen (2008) The reconstruction property in Banach spaces and a perturbation theorem. Canad. Math. Bull., 51(3):348–358. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Asghar Rahimi (2008) Frame properties of wave packet systems in L^2(R^d). Adv. Comput. Math., 29(2):101–111. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Wenchang Sun (2008) Explicitly given pairs of dual frames with compactly supported generators and applications to irregular B-splines. J. Approx. Theory, 151(2):155–163. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2008) Frames and bases. Birkhauser Boston, Inc., Boston, MA http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig (2009) Constructing pairs of dual bandlimited framelets with desired time localization. Adv. Comput. Math., 30(3):231–247. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2010) Functions, spaces, and expansions. Birkhauser Boston, Inc., Boston, MA http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Richard S. Laugesen (2010) Approximately dual frames in Hilbert spaces and applications to Gabor frames. Sampl. Theory Signal Image Process., 9(1-3):77–89. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2010) Pairs of oblique duals in spaces of periodic functions. Adv. Comput. Math., 32(3):353–379. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2010) Gabor windows supported on [-1,1] and compactly supported dual windows. Appl. Comput. Harmon. Anal., 28(1):89–103. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Rae Young Kim (2010) On dual Gabor frame pairs generated by polynomials. J. Fourier Anal. Appl., 16(1):1–16. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2011) Optimally sparse approximations of multivariate functions using compactly supported shearlet frames. SampTA'11 (Singapore, 2011) Proc. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Mads Sielemann Jakobsen (2011) Series representations in L^2(R) of products of trigonometric functions. Normat, 59(1):22–43, 48. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2011) On the duality principle by Casazza, Kutyniok, and Lammers. J. Fourier Anal. Appl., 17(4):640–655. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Mads Sielemann Jakobsen (2011) Dual pairs of Gabor frames for trigonometric generators without the partition of unity property. Asian-Eur. J. Math., 4(4):589–603. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Matcin Bownik and Jakob Lemvig (2011) Affine and quasi-affine frames for rational dilations. Trans. Amer. Math. Soc., 363(4):1887–1924. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Matcin Bownik and Jakob Lemvig (2012) Oversampling of wavelet frames for real dilations. Jour. London Math. Soc., 85:765–788. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Shearlets and Optimally Sparse Approximations. In Shearlets: Multiscale Analysis for Multivariate Data. (D. Labate and G. Kutyniok, Eds.), Springer. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Optimally sparse approximations of 3D functions by compactly supported shearlet frames. SIAM J. Math. Anal., 44(4):2962–3017. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig (2012) Constructing pairs of dual bandlimited frame wavelets in L^2(R^n). Appl. Comput. Harmon. Anal., 32:313–328. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Kristian Berg Thomsen and Mads Paulsen (2012) Gibbs phenomenon swinger in 2D. Normat, 60(1):15–30, 48 (2013). http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Peter Massopust (2012) Exponential B-splines and the partition of unity property. Adv. Comput. Math., 37(3):301–318. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2012) Gabor windows supported on [-1,1] and dual windows with small support. Adv. Comput. Math., 36(4):525–545. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Alex, er M. Powell and Xiang Chun Xiao (2012) A note on finite dual frame pairs. Proc. Amer. Math. Soc., 140(11):3921–3930. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2012) Pairs of dual periodic frames. Appl. Comput. Harmon. Anal., 33(3):315–329. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik, Ole Christensen, Xinli Huang and Baiyun Yu (2012) Extension of shift-invariant systems in L^2(R) to frames. Numer. Funct. Anal. Optim., 33(7-9):833–846. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Compactly supported shearlets. In Approximation Theory XIII: San Antonio 2010.. Springer Proc. Math., 163–186 (13). http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Xiang Chun Xiao and Yu Can Zhu (2013) Characterizing R-duality in Banach spaces. Acta Math. Sin. (Engl. Ser.), 29(1):75–84. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2013) Extensions of Bessel sequences to dual pairs of frames. Appl. Comput. Harmon. Anal., 34(2):224–233. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Lasse Hjuler Christiansen and Ole Christensen (2013) Construction of smooth compactly supported windows generating dual pairs of Gabor frames. Asian-Eur. J. Math., 6(1):1350011, 13. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Elnaz Osgooei (2013) On frame properties for Fourier-like systems. J. Approx. Theory, 172:47–57. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2013) Regularity of dual Gabor windows. Abstr. Appl. Anal.. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Felix Krahmer, Gitta Kutyniok and Jakob Lemvig (2013) Sparsity and spectral properties of dual frames. Linear Algebra Appl., 439(4):982–998. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2014) A short introduction to frames, Gabor systems, and wavelet systems. Azerb. J. Math., 4(1):25–39. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2014) On Parseval wavelet frames with two or three generators via the unitary extension principle. Canad. Math. Bull., 57(2):254–263. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2014) Frames and extension problems I. In Fractals, wavelets, and their applications, 219–234. . Springer, Cham http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2014) From dual pairs of Gabor frames to dual pairs of wavelet frames and vice versa. Appl. Comput. Harmon. Anal., 36(2):198–214. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2014) Frames and extension problems II. In Fractals, wavelets, and their applications, 235–243. . Springer, Cham http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

• Ana Benavente, Ole Christensen and Maria I. Zakowicz (2017) Generalized shift-invariant systems and approximately dual frames. Ann. Funct. Anal., 8(2):177–189. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Diana T. Stoeva and Ole Christensen (2015) On R-duals and the duality principle in Gabor analysis. J. Fourier Anal. Appl., 21(2):383–400. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Diana T. Stoeva and Ole Christensen (2016) On various R-duals and the duality principle. Integral Equations Operator Theory, 84(4):577–590. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Enstad, Ulrik B. R., Mads S. Jakobsen and Luef, Franz (2019) Time-frequency analysis on the adeles over the rationals. C. R. Math. Acad. Sci. Paris, 357(2):188–199. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Felix Krahmer, Gitta Kutyniok and Jakob Lemvig (2013) Sparsity and spectral properties of dual frames. Linear Algebra Appl., 439(4):982–998. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Felix Krahmer, Gitta Kutyniok and Jakob Lemvig (2014) Sparse matrices in frame theory. Comput. Statist., 29(3-4):547–568. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Compactly supported shearlets. In Approximation Theory XIII: San Antonio 2010.. Springer Proc. Math., 163–186 (13). http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2011) Optimally sparse approximations of multivariate functions using compactly supported shearlet frames. SampTA'11 (Singapore, 2011) Proc. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Optimally sparse approximations of 3D functions by compactly supported shearlet frames. SIAM J. Math. Anal., 44(4):2962–3017. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Gitta Kutyniok, Jakob Lemvig and Wang-Q Lim (2012) Shearlets and Optimally Sparse Approximations. In Shearlets: Multiscale Analysis for Multivariate Data. (D. Labate and G. Kutyniok, Eds.), Springer. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Hartmut Führ and Jakob Lemvig (2018) System bandwidth and the existence of generalized shift-invariant frames. J. Funct. Anal.. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig (2017) On some Hermite series identities and their applications to Gabor analysis. Monatsh. Math., 182(4):899–912. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig (2012) Constructing pairs of dual bandlimited frame wavelets in L^2(R^n). Appl. Comput. Harmon. Anal., 32:313–328. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig (2009) Constructing pairs of dual bandlimited framelets with desired time localization. Adv. Comput. Math., 30(3):231–247. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig and Kamilla Haahr Nielsen (2020) Gabor windows supported on {1,1$} and construction of compactly supported dual windows with optimal smoothness. J. Approx. Theory, 249:105304. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig, Christopher Miller and Kasso A. Okoudjou (2014) Prime tight frames. Adv. Comput. Math., 40(2):315–334. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig and Jordy Timo van Velthoven (2020) Criteria for generalized translation-invariant frames. Studia Math., 250(1):31–63. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig and Kamilla Haahr Nielsen (2019) On the smoothness of dual windows for Gabor windows supported on {-1, 1$}. In Sampling Theory and Applications (SampTA), 2019 International Conference on. July http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Jakob Lemvig and Kamilla Haahr Nielsen (2016) Counterexamples to the B-spline conjecture for Gabor frames. J. Fourier Anal. Appl., 22(6):1440–1451. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Lasse Hjuler Christiansen and Ole Christensen (2013) Construction of smooth compactly supported windows generating dual pairs of Gabor frames. Asian-Eur. J. Math., 6(1):1350011, 13. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads S. Jakobsen (2018) On a (no longer) new Segal algebra: a review of the Feichtinger algebra. J. Fourier Anal. Appl., 24(6):1579–1660. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads S. Jakobsen and Luef, Franz (2019) Sampling and periodization of generators of Heisenberg modules. Internat. J. Math., 30(10):1950051, 37. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads Sielemann Jakobsen and Jakob Lemvig (2015) A characterization of tight and dual generalized translation invariant frames. In Sampling Theory and Applications (SampTA), 2015 International Conference on. May, pages 96-100 http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads Sielemann Jakobsen and Jakob Lemvig (2016) Reproducing formulas for generalized translation invariant systems on locally compact abelian groups. Trans. Amer. Math. Soc., 368(12):8447–8480. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads Sielemann Jakobsen and Jakob Lemvig (2016) Co-compact Gabor Systems on Locally Compact Abelian Groups. J. Fourier Anal. Appl., 22(1):36–70. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads Sielemann Jakobsen and Jakob Lemvig (2015) Duality results for co-compact Gabor systems. In Sampling Theory and Applications (SampTA), 2015 International Conference on. May, pages 144-147 http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Mads Sielemann Jakobsen and Jakobsen Lemvig (2016) Density and duality theorems for regular Gabor frames. J. Funct. Anal., 270(1):229–263. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik and Jakob Lemvig (2017) Wavelets for non-expanding dilations and the lattice counting estimate. Int. Math. Res. Not. IMRN. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik and Jakob Lemvig (2016) Wavelets for non-expanding dilations and the lattice counting estimate. Int. Math. Res. Not.. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik and Jakob Lemvig (2007) The canonical and alternate duals of a wavelet frame. Appl. Comput. Harmon. Anal., 23(2):263–272. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik, Mads S. Jakobsen, Jakob Lemvig and Kasso A. Okoudjou (2017) On Wilson bases in L^2(\mathbb R^d). SIAM J. Math. Anal., 49(5):3999–4023. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik, Mads S. Jakobsen, Jakob Lemvig and Kasso A. Okoudjou (2017) On Multivariate Wilson Bases. In Sampling Theory and Applications (SampTA), 2017 International Conference on. July http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik and Ole Christensen (2007) Characterization and perturbation of Gabor frame sequences with rational parameters. J. Approx. Theory, 147(1):67–80. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Marcin Bownik, Ole Christensen, Xinli Huang and Baiyun Yu (2012) Extension of shift-invariant systems in L^2(R) to frames. Numer. Funct. Anal. Optim., 33(7-9):833–846. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Matcin Bownik and Jakob Lemvig (2012) Oversampling of wavelet frames for real dilations. Jour. London Math. Soc., 85:765–788. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Matcin Bownik and Jakob Lemvig (2011) Affine and quasi-affine frames for rational dilations. Trans. Amer. Math. Soc., 363(4):1887–1924. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2017) Differential equations and infinite series. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2006) Frames and generalized shift-invariant systems. In Pseudo-differential operators and related topics, 193–209. . Birkhauser, Basel http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2014) A short introduction to frames, Gabor systems, and wavelet systems. Azerb. J. Math., 4(1):25–39. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2010) Functions, spaces, and expansions. Birkhauser Boston, Inc., Boston, MA http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2014) Six (seven) problems in frame theory. In New perspectives on approximation and sampling theory, 337–358. . Birkhauser/Springer, Cham http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2006) Pairs of dual Gabor frame generators with compact support and desired frequency localization. Appl. Comput. Harmon. Anal., 20(3):403–410. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2008) Frames and bases. Birkhauser Boston, Inc., Boston, MA http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen (2014) Frames and extension problems I. In Fractals, wavelets, and their applications, 219–234. . Springer, Cham http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Alex, er M. Powell and Xiang Chun Xiao (2012) A note on finite dual frame pairs. Proc. Amer. Math. Soc., 140(11):3921–3930. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Asghar Rahimi (2008) Frame properties of wave packet systems in L^2(R^d). Adv. Comput. Math., 29(2):101–111. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Brigitte Forster and Peter Massopust (2015) Directional time--frequency analysis via continuous frames. Bull. Aust. Math. Soc., 92(2):268–281. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Elnaz Osgooei (2013) On frame properties for Fourier-like systems. J. Approx. Theory, 172:47–57. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, H. O. Kim, R. Y. Kim and J. K. Lim (2005) Perturbation of frame sequences in shift-invariant spaces. J. Geom. Anal., 15(2):181–192. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, H. O. Kim, R. Y. Kim and J. K. Lim (2006) Riesz sequences of translates and generalized duals with support on {0,1$}. J. Geom. Anal., 16(4):585–596. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

bibtexquery:[bibfile.bib][50]

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Title: Wavelet Frames and Their Duals (pdf Δ). Supervisor: Ole Christensen. Thesis examiners: Prof. Per Christian Hansen (chairman, DTU), Prof. Say Song Goh (National University of Singapore), Prof. Richard S. Laugesen (University of Illinois, U.S.A.). Thesis defence: Friday September 26, 2008.

Title: Wavelet Frames and Their Duals (pdf Δ). Supervisor: Ole Christensen. Thesis examiners: Prof. Per Christian Hansen (chairman, DTU), Prof. Say Song Goh (National University of Singapore), Prof. Richard S. Laugesen (University of Illinois, U.S.A.). Thesis defence: Friday September 26, 2008.

Ph.D. Thesis

Title: Wavelet Frames and Their Duals (Attach:PDF Δ). Supervisor: Ole Christensen. Thesis examiners: Prof. Per Christian Hansen (chairman, DTU), Prof. Say Song Goh (National University of Singapore), Prof. Richard S. Laugesen (University of Illinois, U.S.A.). Thesis defence: Friday September 26, 2008.

Preprints & 2010 Publications

• Ole Christensen (2010) Functions, spaces, and expansions. Birkhauser Boston, Inc., Boston, MA http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen, Hong Oh Kim and Rae Young Kim (2010) Gabor windows supported on [-1,1] and compactly supported dual windows. Appl. Comput. Harmon. Anal., 28(1):89–103. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Rae Young Kim (2010) On dual Gabor frame pairs generated by polynomials. J. Fourier Anal. Appl., 16(1):1–16. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Richard S. Laugesen (2010) Approximately dual frames in Hilbert spaces and applications to Gabor frames. Sampl. Theory Signal Image Process., 9(1-3):77–89. http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%
• Ole Christensen and Say Song Goh (2010) Pairs of oblique duals in spaces of periodic functions. Adv. Comput. Math., 32(3):353–379. http://www.mat.dtu.dk/people/J.Lemvig/files/world.png %height=13px%http://www.mat.dtu.dk/people/J.Lemvig/files/bibtex.gif%%

2009 Publications