Stability theorems for Fourier frames and wavelet Riesz bases |
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Authors: | Radu Balan |
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Affiliation: | (1) Program in Applied and Computational Mathematics, Princeton University, 08544 Princeton, NJ |
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Abstract: | In this paper we present two applications of a Stability Theorem of Hilbert frames to nonharmonic Fourier series and wavelet Riesz basis. The first result is an enhancement of the Paley-Wiener type constant for nonharmonic series given by Duffin and Schaefer in [6] and used recently in some applications (see [3]). In the case of an orthonormal basis, our estimate reduces to Kadec’ optimal 1/4 result. The second application proves that a phenomenon discovered by Daubechies and Tchamitchian [4] for the orthonormal Meyer wavelet basis (stability of the Riesz basis property under small changes of the translation parameter) actually holds for a large class of wavelet Riesz bases. |
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Keywords: | Primary 42C15 Secondary 41A30 |
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