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Gabor duality characterizations. (English) Zbl 1129.42420
Heil, Christopher (ed.), Harmonic analysis and applications. In Honor of John J. Benedetto. Basel: Birkhäuser (ISBN 0-8176-3778-8/hbk). Applied and Numerical Harmonic Analysis, 127-137 (2006).
Summary: Gabor duality studies have resulted in a number of characterizations of dual Gabor frames, among which the Wexler-Raz identity and the operator approach reformulation by A. J. E. M. Janssen [J. Fourier Anal. Appl. 1, No. 4, 403–436 (1995; (1995; Zbl 0887.42028)] and by I. C. Daubechies, H. J. Landau and Z. A. Landau [J. Fourier Anal. Appl. 1, No. 4, 437–478 (1995; Zbl 0888.47018)] are well known. A concise overview of existing Gabor duality characterizations is presented. In particular, we demonstrate that the Gabor duality conditions by J. Wexler and S. Raz [Signal Process. 21, No. 3, 207–220 (1991)] and by Daubechies, Landau and Landau [loc. cit.], and the parametric dual Gabor formula of S. Li [Numer. Funct. Anal. Optim. 16, No. 9–10, 1181–1191 (1995; Zbl 0849.42023)], are equivalent.
For the entire collection see [Zbl 1095.00007].

MSC:
42C15 General harmonic expansions, frames
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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