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Stability theorems for Fourier frames and wavelet Riesz bases

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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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  1. Program in Applied and Computational Mathematics, Princeton University, 08544, Princeton, NJ

    Radu Balan

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  1. Radu Balan
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Balan, R. Stability theorems for Fourier frames and wavelet Riesz bases. The Journal of Fourier Analysis and Applications 3, 499–504 (1997). https://doi.org/10.1007/BF02648880

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