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Localization of Frames,Banach Frames,and theInvertibility of the FrameOperator |
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| Authors: | Karlheinz?Gr?chenig mailto:groch@math.uconn.edu" title=" groch@math.uconn.edu" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author |
| Affiliation: | (1) Department of Mathematics, The University of Connecticut, Storrs, CT 06269-3009, USA |
| Abstract: | We introduce a new concept to describe the localization of frames. In our mainresult we show that the frame operator preserves this localization and that the dual frame possessesthe same localization property. As an application we show that certain frames for Hilbert spacesextend automatically to Banach frames. Using this abstract theory, we derive new results on theconstruction of nonuniform Gabor frames and solve a problem about non-uniform sampling inshift-invariant spaces. |
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