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Selected Publications by Ole Christensen

  • Christensen, O., Hasannasab, M. and Philipps, F. (2018) Frame properties of operator orbits. (preprint). BibTeX
  • Ole Christensen and Marzieh Hasannasab (2017) Frames, operator representations, and open problems. In Proceedings of IWOTA 2017. BibTeX
  • Ole Christensen (2017) Differential equations and infinite series. BibTeX
  • 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 BibTeX
  • Christensen, Ole and Hasannasab, Marzieh (2017) Operator representations of frames: boundedness, duality, and stability. Integral Equations Operator Theory, 88(4):483–499. Journal version BibTeX
  • Massopust, Peter, Forster, Brigitte and Christensen, Ole (2017) Fractional and complex pseudo-splines and the construction of Parseval frames. Appl. Math. Comput., 314:12–24. Journal version BibTeX
  • Benavente, Ana, Christensen, Ole and Zakowicz, Mar\'\i a I. (2017) Generalized shift-invariant systems and approximately dual frames. Ann. Funct. Anal., 8(2):177–189. Journal version BibTeX
  • Christensen, Ole, Kim, Hong Oh and Kim, Rae Young (2017) Characterisations of partition of unities generated by entire functions in \mathbb C^d. Bull. Aust. Math. Soc., 95(2):281–290. Journal version BibTeX
  • 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. Journal version BibTeX
  • Christensen, Ole and Goh, Say Song (2017) Construction of Scaling Partitions of Unity. Frontiers in Applied Mathematics and Statistics, 3:21. Journal version BibTeX
  • Ole Christensen and Say Song Goh (2017) The unitary extension principle on locally compact abelian groups. Applied and Computational Harmonic Analysis. Journal version BibTeX
  • Christensen, O., Hasannasab, M. and Stoeva, D. T. (2017) Operator representations of sequences and dynamical sampling. (preprint). BibTeX
  • Christensen, O., Janssen, A. E. J. M., Kim, H.O., Kim, R.Y. (2017) Approximately dual frames and almost perfect reconstruction basedon a class of window functions. (preprint). BibTeX
  • Christensen, Ole, Kim, Hong Oh and Kim, Rae Young (2017) B-Spline Approximations of the Gaussian, their Gabor Frame Properties, and Approximately Dual Frames. Journal of Fourier Analysis and Applications. Journal version BibTeX
  • Christensen, O., Hasannasab, O. and Rashidi, E. (2017) Dynamical sampling and frame representations with boundedoperators. (preprint). BibTeX
  • Christensen, Ole and Hasannasab, Marzieh (2017) Gabor Frames in \ell^2(\mathbb Z) and Linear Dependence. Journal of Fourier Analysis and Applications. Journal version BibTeX
  • Ole Christensen and Say Song Goh (2017) The unitary extension principle on locally compact abelian groups. Applied and Computational Harmonic Analysis. Journal version BibTeX
  • Christensen, Ole, Kim, Hong Oh and Kim, Rae Young (2016) On the Gabor frame set for compactly supported continuous functions. J. Inequal. Appl.. Journal version BibTeX
  • Ole Christensen, Marzieh Hasannasab (2016) Frame properties of systems arising via iterated actions of operators. (submitted, arXiv: 1704.08918, 2016). Journal version BibTeX
  • Stoeva, Diana T. and Christensen, Ole (2016) On various R-duals and the duality principle. Integral Equations Operator Theory, 84(4):577–590. Journal version BibTeX
  • Christensen, Ole, Kim, Hong Oh and Kim, Rae Young (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. Journal version BibTeX
  • 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. Journal version BibTeX
  • Ole Christensen and Say Song Goh (2015) Fourier-like frames on locally compact abelian groups. J. Approx. Theory, 192:82–101. Journal version BibTeX
  • Ole Christensen, Brigitte Forster and Peter Massopust (2015) Directional time--frequency analysis via continuous frames. Bull. Aust. Math. Soc., 92(2):268–281. Journal version BibTeX
  • 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. Journal version BibTeX
  • 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. Journal version BibTeX
  • Ole Christensen (2014) A short introduction to frames, Gabor systems, and wavelet systems. Azerb. J. Math., 4(1):25–39. BibTeX
  • 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. Journal version BibTeX
  • 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. Journal version BibTeX
  • Ole Christensen (2014) Frames and extension problems I. In Fractals, wavelets, and their applications, 219–234. . Springer, Cham Journal version BibTeX
  • Ole Christensen (2014) Six (seven) problems in frame theory. In New perspectives on approximation and sampling theory, 337–358. . Birkhauser/Springer, Cham BibTeX
  • 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 Journal version BibTeX
  • Ole Christensen, Hong Oh Kim and Rae Young Kim (2013) Regularity of dual Gabor windows. Abstr. Appl. Anal.. BibTeX
  • Ole Christensen and Elnaz Osgooei (2013) On frame properties for Fourier-like systems. J. Approx. Theory, 172:47–57. Journal version BibTeX
  • 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. Journal version BibTeX
  • 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. Journal version BibTeX
  • 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. Journal version BibTeX
  • 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. Journal version BibTeX
  • 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. Journal version BibTeX
  • Ole Christensen and Say Song Goh (2012) Pairs of dual periodic frames. Appl. Comput. Harmon. Anal., 33(3):315–329. Journal version BibTeX
  • Ole Christensen and Peter Massopust (2012) Exponential B-splines and the partition of unity property. Adv. Comput. Math., 37(3):301–318. Journal version BibTeX
  • Ole Christensen, Kristian Berg Thomsen and Mads Paulsen (2012) Gibbs phenomenon swinger in 2D. Normat, 60(1):15–30, 48 (2013). BibTeX
  • 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. Journal version BibTeX
  • 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. Journal version BibTeX
  • Ole Christensen and Mads Sielemann Jakobsen (2011) Series representations in L^2(R) of products of trigonometric functions. Normat, 59(1):22–43, 48. BibTeX
  • 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. Journal version BibTeX
  • 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. Journal version BibTeX
  • Ole Christensen and Rae Young Kim (2010) On dual Gabor frame pairs generated by polynomials. J. Fourier Anal. Appl., 16(1):1–16. Journal version BibTeX
  • Ole Christensen and Say Song Goh (2010) Pairs of oblique duals in spaces of periodic functions. Adv. Comput. Math., 32(3):353–379. Journal version BibTeX
  • 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. BibTeX
  • Ole Christensen (2010) Functions, spaces, and expansions. Birkhauser Boston, Inc., Boston, MA Journal version BibTeX
  • 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. Journal version BibTeX
  • Peter G. Casazza and Ole Christensen (2008) The reconstruction property in Banach spaces and a perturbation theorem. Canad. Math. Bull., 51(3):348–358. Journal version BibTeX
  • Ole Christensen (2008) Frames and bases. Birkhauser Boston, Inc., Boston, MA Journal version BibTeX
  • Ole Christensen and Asghar Rahimi (2008) Frame properties of wave packet systems in L^2(R^d). Adv. Comput. Math., 29(2):101–111. Journal version BibTeX
  • Marcin Bownik and Ole Christensen (2007) Characterization and perturbation of Gabor frame sequences with rational parameters. J. Approx. Theory, 147(1):67–80. Journal version BibTeX
  • Ole Christensen (2006) Pairs of dual Gabor frame generators with compact support and desired frequency localization. Appl. Comput. Harmon. Anal., 20(3):403–410. Journal version BibTeX
  • Ole Christensen (2006) Frames and generalized shift-invariant systems. In Pseudo-differential operators and related topics, 193–209. . Birkhauser, Basel Journal version BibTeX
  • Ole Christensen and Wenchang Sun (2006) Stability of wavelet frames with matrix dilations. Proc. Amer. Math. Soc., 134(3):831–842 (electronic). Journal version BibTeX
  • 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. Journal version BibTeX
  • Ole Christensen and Khadija L. Christensen (2006) Linear independence and series expansions in function spaces. Amer. Math. Monthly, 113(7):611–627. Journal version BibTeX
  • 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. Journal version BibTeX
  • Yonina C. Eldar and Ole Christensen (2006) Characterization of oblique dual frame pairs. EURASIP J. Appl. Signal Process.. BibTeX
  • 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 Journal version BibTeX
  • 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. Journal version BibTeX
  • Ole Christensen and Khadija L. Christensen (2005) Approximation theory. Birkhauser Boston, Inc., Boston, MA Journal version BibTeX
  • Ole Christensen and Yonina C. Eldar (2005) Generalized shift-invariant systems and frames for subspaces. J. Fourier Anal. Appl., 11(3):299–313. Journal version BibTeX