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Proceedings Paper

Duality principles, localization of frames, and Gabor theory
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Paper Abstract

The theory of localized frames is a recently introduced concept with broad implications to frame theory in general, as well as to the special cases of Gabor and wavelet frames. Using the new notion of a R-dual sequence associated with a Bessel sequence, we derive several duality principles concerning localization in abstract frame theory. As applications of our results we prove a duality principle of localization of Gabor systems in the spirit of the Ron-Shen duality principle, and obtain a Janssen representation for general frame operators.

Paper Details

Date Published: 17 September 2005
PDF: 9 pages
Proc. SPIE 5914, Wavelets XI, 591418 (17 September 2005); doi: 10.1117/12.615440
Show Author Affiliations
Peter G. Casazza, Univ. of Missouri, Columbia (United States)
Gitta Kutyniok, Justus-Liebig-Univ. Giessen (Germany)
Mark C. Lammers, Univ. of North Carolina at Wilmington (United States)

Published in SPIE Proceedings Vol. 5914:
Wavelets XI
Manos Papadakis; Andrew F. Laine; Michael A. Unser, Editor(s)

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