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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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: Let $\psi$ be a frame vector under the action of a collection of unitary operators $\mathcal U$. 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

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