Localization of Frames,Banach Frames,and the
Invertibility of the Frame
Operator |
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Authors: | Email author" target="_blank">Karlheinz?Gr?chenigEmail author |
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Institution: | (1) Department of Mathematics, The University of Connecticut, Storrs, CT 06269-3009, USA |
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Abstract: | We introduce a new concept to describe the localization of frames. In our main
result we show that the frame operator preserves this localization and that the dual frame possesses
the same localization property. As an application we show that certain frames for Hilbert spaces
extend automatically to Banach frames. Using this abstract theory, we derive new results on the
construction of nonuniform Gabor frames and solve a problem about non-uniform sampling in
shift-invariant spaces. |
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Keywords: | |
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