A unified characterization of reproducing systems generated by a finite family (Q1608538)
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scientific article; zbMATH DE number 1777211
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A unified characterization of reproducing systems generated by a finite family |
scientific article; zbMATH DE number 1777211 |
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A unified characterization of reproducing systems generated by a finite family (English)
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8 August 2002
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Let \(C\) be a nonsingular \(n\times n\) matrix with real entries. Given a collection of functions \(\{g_p\}_{p\in P}\) in \(L^2(\mathbb{R}^n)\), tight frames of the form \(\{g_p(\cdot -Ck)\}_{k\in \mathbb{Z}^n, p\in P}\) are characterized. Furthermore, equivalent conditions for two systems of this type to be dual frames are given. The results are applied to wavelet systems and Gabor systems.
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tight frames
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dual frames
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wavelet systems
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Gabor systems
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