期刊
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
卷 10, 期 2, 页码 105-132出版社
SPRINGER BIRKHAUSER
DOI: 10.1007/s00041-004-8007-1
关键词
frame; Banach frame; Jaffard's lemma; sampling theorems; non uniform sampling; shift-invariant spaces; nonuniform Gabor frame; phase space analysis; symbolic calculus
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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