Publications
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Preprints
- Ole Christensen, Marzieh Hasannasab and Friedrich Philipp (2018) Frame properties of operator orbits. (preprint).
2020 Publications
- Jakob Lemvig and Kamilla Haahr Nielsen (2020) Gabor windows supported on {1,1$} and construction of compactly supported dual windows with optimal smoothness. J. Approx. Theory, 249:105304.
- Jakob Lemvig and Jordy Timo van Velthoven (2020) Criteria for generalized translation-invariant frames. Studia Math., 250(1):31–63.
2019 Publications
- Enstad, Ulrik B. R., Mads S. Jakobsen and Luef, Franz (2019) Time-frequency analysis on the adeles over the rationals. C. R. Math. Acad. Sci. Paris, 357(2):188–199.
- Jakob Lemvig and Kamilla Haahr Nielsen (2019) On the smoothness of dual windows for Gabor windows supported on {-1, 1$}. In Sampling Theory and Applications (SampTA), 2019 International Conference on. July
- Mads S. Jakobsen and Luef, Franz (2019) Sampling and periodization of generators of Heisenberg modules. Internat. J. Math., 30(10):1950051, 37.
- Ole Christensen and Marzieh Hasannasab (2019) Gabor frames in \ell^2(\mathbb Z) and linear dependence. J. Fourier Anal. Appl., 25(1):101–107.
- Ole Christensen and Marzieh Hasannasab (2019) Frame properties of systems arising via iterated actions of operators. Appl. Comput. Harmon. Anal., 46(3):664–673.
- Ole Christensen and Say Song Goh (2019) The unitary extension principle on locally compact abelian groups. Appl. Comput. Harmon. Anal., 47(1):1–29.
2018 Publications
- Hartmut Führ and Jakob Lemvig (2018) System bandwidth and the existence of generalized shift-invariant frames. J. Funct. Anal..
- 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.
- 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.
- 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.
- 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
- 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.
- Ole Christensen, Marzieh Hasannasab and Ehsan Rashidi (2018) Dynamical sampling and frame representations with bounded operators. J. Math. Anal. Appl., 463(2):634–644.
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.
- Jakob Lemvig (2017) On some Hermite series identities and their applications to Gabor analysis. Monatsh. Math., 182(4):899–912.
- Marcin Bownik and Jakob Lemvig (2017) Wavelets for non-expanding dilations and the lattice counting estimate. Int. Math. Res. Not. IMRN.
- 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
- 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.
- Ole Christensen (2017) Differential equations and infinite series.
- 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.
- Ole Christensen and Marzieh Hasannasab (2017) Operator representations of frames: boundedness, duality, and stability. Integral Equations Operator Theory, 88(4):483–499.
- 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
- Ole Christensen and Say Song Goh (2017) Construction of Scaling Partitions of Unity. Frontiers in Applied Mathematics and Statistics, 3:21.
- 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.
- 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.
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.
- Jakob Lemvig and Kamilla Haahr Nielsen (2016) Counterexamples to the B-spline conjecture for Gabor frames. J. Fourier Anal. Appl., 22(6):1440–1451.
- 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.
- Mads Sielemann Jakobsen and Jakob Lemvig (2016) Co-compact Gabor Systems on Locally Compact Abelian Groups. J. Fourier Anal. Appl., 22(1):36–70.
- Mads Sielemann Jakobsen and Jakobsen Lemvig (2016) Density and duality theorems for regular Gabor frames. J. Funct. Anal., 270(1):229–263.
- Marcin Bownik and Jakob Lemvig (2016) Wavelets for non-expanding dilations and the lattice counting estimate. Int. Math. Res. Not..
- 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.
- Ole Christensen, Hong Oh Kim and Rae Young Kim (2016) On the Gabor frame set for compactly supported continuous functions. J. Inequal. Appl..
2015 Publications
- 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.
- 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
- 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
- Ole Christensen, Brigitte Forster and Peter Massopust (2015) Directional time--frequency analysis via continuous frames. Bull. Aust. Math. Soc., 92(2):268–281.
- 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.
- 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.
- Ole Christensen and Say Song Goh (2015) Fourier-like frames on locally compact abelian groups. J. Approx. Theory, 192:82–101.
2014 Publications
- Felix Krahmer, Gitta Kutyniok and Jakob Lemvig (2014) Sparse matrices in frame theory. Comput. Statist., 29(3-4):547–568.
- Jakob Lemvig, Christopher Miller and Kasso A. Okoudjou (2014) Prime tight frames. Adv. Comput. Math., 40(2):315–334.
- Ole Christensen (2014) Frames and extension problems I. In Fractals, wavelets, and their applications, 219–234. . Springer, Cham
- Ole Christensen (2014) Six (seven) problems in frame theory. In New perspectives on approximation and sampling theory, 337–358. . Birkhauser/Springer, Cham
- Ole Christensen (2014) A short introduction to frames, Gabor systems, and wavelet systems. Azerb. J. Math., 4(1):25–39.
- 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
- 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.
- 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.
2013 Publications
- Felix Krahmer, Gitta Kutyniok and Jakob Lemvig (2013) Sparsity and spectral properties of dual frames. Linear Algebra Appl., 439(4):982–998.
- 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.
- Ole Christensen and Elnaz Osgooei (2013) On frame properties for Fourier-like systems. J. Approx. Theory, 172:47–57.
- Ole Christensen, Hong Oh Kim and Rae Young Kim (2013) Regularity of dual Gabor windows. Abstr. Appl. Anal..
- 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.
- 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.