Banach Framed, Decay in the Context of Localization

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 May 2007 English Publisher:Springer Science and Business Media LLCJournal:Sampling Theory in Signal and Image Processing, volume 6, pages 151-166 (issn: 1530-6429,

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Authors: Fumiko Futamura;

doi: 10.1007/bf03549469

Banach Framed, Decay in the Context of Localization

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Abstract

We introduce a new definition of localization for frames which eliminates the dependence on the indexing of the frames. Two main results of Grochenig are extended to this definition, namely that the dual of a localized frame is also localized, and a frame localized with respect to another frame is a Banach frame for the associated family of Banach spaces. These results parallel the results of a more recent paper by Fornasier and Grochenig.

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Vanderbilt University
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