Approximations for Gabor and wavelet frames

Author:
Deguang Han

Journal:
Trans. Amer. Math. Soc. **355** (2003), 3329-3342

MSC (2000):
Primary 42C15, 46C05, 47B10

DOI:
https://doi.org/10.1090/S0002-9947-03-03047-2

Published electronically:
April 24, 2003

MathSciNet review:
1974690

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a frame vector under the action of a collection of unitary operators . Motivated by the recent work of Frank, Paulsen and Tiballi and some application aspects of Gabor and wavelet frames, we consider the existence and uniqueness of the best approximation by normalized tight frame vectors. We prove that for any frame induced by a projective unitary representation for a countable discrete group, the best normalized tight frame (NTF) approximation exists and is unique. Therefore it applies to Gabor frames (including Gabor frames for subspaces) and frames induced by translation groups. Similar results hold for semi-orthogonal wavelet frames.

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Additional Information

**Deguang Han**

Affiliation:
Department of Mathematics, University of Central Florida, Orlando, Florida 38216

Email:
dhan@pegasus.cc.ucf.edu

DOI:
https://doi.org/10.1090/S0002-9947-03-03047-2

Keywords:
Hilbert spaces,
frames,
unitary systems,
approximation,
Gabor family and Gabor frames,
wavelet frames.

Received by editor(s):
February 19, 2002

Published electronically:
April 24, 2003

Article copyright:
© Copyright 2003
American Mathematical Society