Duality principles, localization of frames, and Gabor theory
نویسندگان
چکیده
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.
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