Frames, Riesz bases, and discrete Gabor/wavelet expansions (Q2718942)
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scientific article; zbMATH DE number 1597837
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Frames, Riesz bases, and discrete Gabor/wavelet expansions |
scientific article; zbMATH DE number 1597837 |
Statements
Frames, Riesz bases, and discrete Gabor/wavelet expansions (English)
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14 May 2001
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frames
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Riesz basis
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wavelets
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Gabor analysis
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complex exponentials
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In this paper the author presents some recent results in frame and Riesz basis theory. The survey is structured in four parts: the first part contains the abstract theory of frames and Riesz bases, and the remaining three parts are devoted to, respectively, frames of (complex) exponentials, Gabor frames, and wavelet frames. Most of the results are necessary and sufficient conditions to have coherent frames. Along the way, the author presents also two open problems, namely the characterization of irregular Gabor frames, and the independence of finite arbitrary time-frequency translates of non-zero \(L^2\)-functions.
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