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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Approximations for Gabor and wavelet frames
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by Deguang Han PDF
Trans. Amer. Math. Soc. 355 (2003), 3329-3342 Request permission

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.
References
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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
  • Received by editor(s): February 19, 2002
  • Published electronically: April 24, 2003
  • © Copyright 2003 American Mathematical Society
  • 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
  • MathSciNet review: 1974690