Duality principles, localization of frames, and Gabor theory

Peter G. Casazza; Gitta Kutyniok; Mark C. Lammers

doi:10.1117/12.615440

17 September 2005 Duality principles, localization of frames, and Gabor theory

Peter G. Casazza, Gitta Kutyniok, Mark C. Lammers

Proceedings Volume 5914, Wavelets XI; 591418 (2005) https://doi.org/10.1117/12.615440
Event: Optics and Photonics 2005, 2005, San Diego, California, United States

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.

Citation Download Citation

Peter G. Casazza, Gitta Kutyniok, and Mark C. Lammers "Duality principles, localization of frames, and Gabor theory", Proc. SPIE 5914, Wavelets XI, 591418 (17 September 2005); https://doi.org/10.1117/12.615440

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