HATA - DTU; Harmonic Analysis - Theory And Applications; Department of Mathematics; Technical University of Denmark

Selected Publications by Ole Christensen

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 Marzieh Hasannasab (2019) Gabor frames in \ell^2(\mathbb Z) and linear dependence. J. Fourier Anal. Appl., 25(1):101–107.
Ole Christensen and Say Song Goh (2019) The unitary extension principle on locally compact abelian groups. Appl. Comput. Harmon. Anal., 47(1):1–29.
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 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 Ehsan Rashidi (2018) Dynamical sampling and frame representations with bounded operators. J. Math. Anal. Appl., 463(2):634–644.
Ole Christensen, Marzieh Hasannasab and Friedrich Philipp (2018) Frame properties of operator orbits. (preprint).
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, 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, 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.
Ana Benavente, Ole Christensen and Maria I. Zakowicz (2017) Generalized shift-invariant systems and approximately dual frames. Ann. Funct. Anal., 8(2):177–189.
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 (2017) Differential equations and infinite series.
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 Marzieh Hasannasab (2017) Operator representations of frames: boundedness, duality, and stability. Integral Equations Operator Theory, 88(4):483–499.
Ole Christensen and Say Song Goh (2017) Construction of Scaling Partitions of Unity. Frontiers in Applied Mathematics and Statistics, 3:21.
Diana T. Stoeva and Ole Christensen (2016) On various R-duals and the duality principle. Integral Equations Operator Theory, 84(4):577–590.
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..
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.
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.
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, Brigitte Forster and Peter Massopust (2015) Directional time--frequency analysis via continuous frames. Bull. Aust. Math. Soc., 92(2):268–281.
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.
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) On Parseval wavelet frames with two or three generators via the unitary extension principle. Canad. Math. Bull., 57(2):254–263.
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, 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 (2013) Regularity of dual Gabor windows. Abstr. Appl. Anal..
Ole Christensen and Elnaz Osgooei (2013) On frame properties for Fourier-like systems. J. Approx. Theory, 172:47–57.
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.
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, 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, 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.
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.
Ole Christensen and Say Song Goh (2012) Pairs of dual periodic frames. Appl. Comput. Harmon. Anal., 33(3):315–329.
Ole Christensen and Peter Massopust (2012) Exponential B-splines and the partition of unity property. Adv. Comput. Math., 37(3):301–318.
Ole Christensen, Kristian Berg Thomsen and Mads Paulsen (2012) Gibbs phenomenon swinger in 2D. Normat, 60(1):15–30, 48 (2013).
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.
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.
Ole Christensen and Mads Sielemann Jakobsen (2011) Series representations in L^2(R) of products of trigonometric functions. Normat, 59(1):22–43, 48.
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.
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.
Ole Christensen and Rae Young Kim (2010) On dual Gabor frame pairs generated by polynomials. J. Fourier Anal. Appl., 16(1):1–16.
Ole Christensen and Say Song Goh (2010) Pairs of oblique duals in spaces of periodic functions. Adv. Comput. Math., 32(3):353–379.
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.
Ole Christensen (2010) Functions, spaces, and expansions. Birkhauser Boston, Inc., Boston, MA
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.
Peter G. Casazza and Ole Christensen (2008) The reconstruction property in Banach spaces and a perturbation theorem. Canad. Math. Bull., 51(3):348–358.
Ole Christensen (2008) Frames and bases. Birkhauser Boston, Inc., Boston, MA
Ole Christensen and Asghar Rahimi (2008) Frame properties of wave packet systems in L^2(R^d). Adv. Comput. Math., 29(2):101–111.
Marcin Bownik and Ole Christensen (2007) Characterization and perturbation of Gabor frame sequences with rational parameters. J. Approx. Theory, 147(1):67–80.
Ole Christensen (2006) Pairs of dual Gabor frame generators with compact support and desired frequency localization. Appl. Comput. Harmon. Anal., 20(3):403–410.
Ole Christensen (2006) Frames and generalized shift-invariant systems. In Pseudo-differential operators and related topics, 193–209. . Birkhauser, Basel
Ole Christensen and Wenchang Sun (2006) Stability of wavelet frames with matrix dilations. Proc. Amer. Math. Soc., 134(3):831–842 (electronic).
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.
Ole Christensen and Khadija L. Christensen (2006) Linear independence and series expansions in function spaces. Amer. Math. Monthly, 113(7):611–627.
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.
Yonina C. Eldar and Ole Christensen (2006) Characterization of oblique dual frame pairs. EURASIP J. Appl. Signal Process..
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
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.
Ole Christensen and Khadija L. Christensen (2005) Approximation theory. Birkhauser Boston, Inc., Boston, MA
Ole Christensen and Yonina C. Eldar (2005) Generalized shift-invariant systems and frames for subspaces. J. Fourier Anal. Appl., 11(3):299–313.