Ole Christensen, Reader

Address:
Department of Mathematics
Matematiktorvet, Building 303
Technical University of Denmark
DK-2800 Kgs. Lyngby
Denmark

Room: 104
Telephone (Direct): (+45) 4525 3043
Telephone (Operator): (+45) 4525 3031
Fax: (+45) 4588 1399
E-mail:

Kursus 01032 - E97

Research interests:

Frames and bases in Hilbert spaces
Gabor analysis
Wavelets
Functional analysis

Research collaboration:

P. Casazza, University of Missouri-Columbia, USA

S. Favier/Felipe Zo, University of San Luis, Argentina

C. Heil, Georgia Tech., USA

A. Lindner, Technical University of Munich, Germany

Wenchang Sun, Nankai University

Hong Oh Kim, KAIST, Korea

Rae Young Kim, Yeungnam University, Korea

Say Song Goh, National University of Singapore

NUHAG, University of Vienna, Austria

Interesting links:

Link to

Further Information:

Short CV:

Born oct. 12, 1966

M.SC, University of Aarhus, 1990.

Ph.D., University of Aarhus, 1993

Assistent professor at the Technical University of Denmark, 1996-1997.

Visiting professor, Georgia Tech and University of Missouri-Columbia, jan. 1997- aug. 1998 (SNF)

Associate professor, Technical University of Denmark, sept. 1998-2006

Dr.scient, 2002

Professor (Docent) at the Technical University of Denmark, 2007 -

Publications:

Several of my publications can be down loaded from the NUHAG server.

Books:

An introduction to frames and Riesz bases. Birkh\"auser 2003. 440 pages.

(with Christensen, K. L.): From Taylor polynomials to wavelets; classical and modern approximation theory. Birkh\"auser Boston, 2004. 156 pages.

(to appear) Frames and bases in mathematics and engineering. Birkh\"auser 2007. Ca. 320 pages.

Journal papers:

Frames and the projection method. Appl. Comp. Harm Anal., 1 (1993), 50-53 .

Frames and pseudo-inverses. J. Math. Anal. Appl. 195 no.2 (1995), 401-414.

Frame perturbations. Proc. Amer. Math. Soc. 123 (1995) 1217-1220.

A Paley-Wiener theorem for frames. Proc. Amer. Math. Soc. 123 (1995), 2199-2202.

(with Hans Feichtinger, Thomas Strohmer) A group-theoretical approach to Gabor analysis. Opt. Engineering 34 no. 6 (1995) , 1697-1704.

Atomic decomposition via projective group representations. Rocky Mountain J. Math. 26 no. 4 (1996), 1289-1312.

Moment problems for frames and applications to irregular sampling and Gabor frames. Appl. Comp. Harm. Anal., 3 (1996) 82-86.

Frames containing a Riesz basis and approximation of the frame coefficients using finite dimensional methods. J. Math. Anal. Appl. 199 (1996) 256-270.

(with Peter G. Casazza) Hilbert space frames containing a Riesz basis and Banach spaces which have no subspace isomorphic to $c_0$. J. Math. Anal. Appl. 202 (1996) 940-950.

(with Christopher Heil) Perturbation of Banach frames and atomic decomposition. Math. Nach. 185 (1997) 33-47.

(with Peter G. Casazza) Perturbation of operators and applications to frame theory. J. Fourier Anal. Appl. 3 (1997), 543-557 (special frame issue).

(with Peter G. Casazza) Approximation of the frame coefficients using finite dimensional methods. Invited paper, special issue ``Best papers on advances in mathematical imaging'' of J. Elec. Imag., 6 (1997), 479-483.

(with Peter G. Casazza) Frames containing a Riesz basis and preservation of this property under perturbation. SIAM J. Math. Anal. 29 no.1 (1998) 266-278.

(with Peter G. Casazza) Riesz frames and approximation of the frame coefficients. Approximation Theory and Its Applications 14 no. 2 (1998), 1-11.

Operators with closed range and perturbation of frames for a subspace. Canad. Math. Bull 42 no.1 (1999) 37-45.

(with Baiqiao Deng and Christopher Heil) Density of Gabor frames. Appl. Comp. Harm. Anal. 7 (1999), 292-304.

(with Peter G. Casazza, A.J.E.M. Janssen) Classifying tight Weyl-Heisenberg frames. Contemp. Math. 247 (1999), 131-148.

Finite-dimensional approximation of the inverse frame operator and applications to Weyl-Heisenberg frames and wavelet frames. J. Fourier Anal. Appl. 6 no.1 (2000), 79-91.

(with Peter G. Casazza) Approximation of the inverse frame operator and applications to Weyl-Heisenberg frames. J. Approx. Theory 103 no.2 (2000), 338-356.

(with Christine deFlitch, Christopher Lennard) Perturbation of frames for a subspace of a Hilbert space. Rocky Mountain J. Math. 30 no. 4 (2000), 1237-1249.

(with Sergio Favier and Felipe Z\'o) Irregular wavelet frames and Gabor frames. Appr. Theory and Its Appl. 17 no. 3 (2001), 90-101.

(with Alexander Lindner) Frames of exponentials: lower frame bounds for finite subfamilies, and approximation of the inverse frame operator. Lin. Alg. and Its Applications 323 no. 1-3 (2001), 117-130

(with Alexander Lindner) Lower bounds for finite Gabor and wavelet systems. Appr. Theory and its Appl. 17 no.1 (2001), 18-29.

(with Peter G. Casazza) Weyl-Heisenberg frames for subspaces of $L^2(R)$. Proc. Amer. Math. Soc. 129 (2001), 145-154.

Frame approximation of pseudo-inverse operators. J. Math. Anal. Appl.{\bf 261} (2001), 45-52.

Frames constructed as linear combination of the elements in a frame. Zeitschrift f\"ur Analysis und ihre Anwendungen, 20 no. 4 (2001), 805-815.

Frames, bases, and discrete Gabor/wavelet expansions. Bull. Amer. Math. Soc. 38 no.3 (2001), 273-291.

(with Peter G. Casazza, A.J.E.M. Janssen) Weyl-Heisenberg frames, translation invariant systems, and the Walnut representation. J. Funct. Anal. 180 no. 1 (2001), 85-147.

(with Peter Casazza, Nigel Kalton) Frames of translates. Collectanea Mathematica 52 no. 1 (2001), 35-54.

(with Peter Casazza, Shidong Li, Alexander Lindner) On Riesz-Fischer sequences and lower frame bounds. Zeitschrift f\"ur Analysis und ihre Anwendungen 21 no. 2 (2002), 305--314.

(with Peter Casazza, Mark Lammers) Perturbations of Weyl-Heisenberg frames. Hokkaido Math. Journal 31 no. 3 (2002), 539-553.

(with Alexander Lindner) Decomposition of Riesz frames and wavelets into a finite union of linearly independent sets. Linear Algebra and Its Appl. 335 (2002), 147-159.

(with Diana T. Stoeva) $p$-frames in separable Banach spaces. Adv. in Comp. Math. 18 (2003), 117-126 (special frame issue).

On frames and multiresolution analysis. The Arabian Journal for Science and Engineering 28 no. 1C (2003), 59--72 (special issue on wavelets, invited paper).

(with Peter G. Casazza) Gabor frames over irregular lattices. Adv. in Comp. Math. 18 (2003), 329-344 (special frame issue).

(with Peter Casazza, Alexander Lindner, Roman Vershynin) Frames and the Feichtinger conjecture. Proc. Amer. Math. Soc. 133 (2005), 1025--1033.

(with Peter Casazza, Diana T. Stoeva) Frame expansions in Banach spaces. J. Math. Anal. Appl. 307} (2005, 710--723.

(with Thomas Strohmer) The finite section method and problems in frame theory. J. Approx. Theory 133 (2005), 221--237.

(with Eldar, Y.) Oblique dual frames and shift-invariant spaces. Appl. Comp. Harm. Anal. 2004 17 no. 1 (2004), 48--68. (special frame issue).

(with Eldar, Y.) Frames for subspaces and generalized duals. J. Fourier Anal. Appl. 11 no. 3 (2005), 299-313.

(with Sun, W.) Stability of wavelet frames with matrix dilations. Proc. Amer. Math. Soc. 134 no. 3 (2006), 831--842.

(with Eldar, Y.) Characterization of oblique dual frame pairs. J. Appl. Signal. Proc. (2006) 1--11 (special frame issue)

(with Kim, O.H., Kim, R. Y., and Lim J. K.) Perturbation of frame sequences in shift-invariant spaces. J. Geometric Analysis 15 no 2 (2005), 181--191.

(with Kim, O.H., Kim, R. Y., and Lim J. K.) Riesz sequences of translates and their generalized duals. J. Geometric Analysis 16 no. 4 (2006), 585-596.

Pairs of dual Gabor frames with compact support and desired frequency localization. Appl. Comp. Harm. Anal. 20 (2006), 403--410.

(with Kim, R.Y.) Pairs of explicitly given dual Gabor frames in $L^2(R^d)$. J. Fourier Anal. Appl. 12 vol. 3 (2006), 243--255.

(with Casazza, P.) A perturbation theorem for Banach spaces. To appear in Can. Bulletin Math., 2007.

(with Bownik, M.) Characterization and perturbation of Gabor frame sequences with rational parameters. J. Approx. theory, to appear 2007.

(with Kim, R.Y.) Tight matrix-generated Gabor frames in $L^2(R^d)$ with desired time-frequency localization.Submitted, 2006.

(with Rahimi, A.) Frame properties of wave packet systems in $L^2(R^d)$. To appear in Adv. Comp. Math. 2007