Article

Journal of Fourier Analysis and Applications

, Volume 3, Issue 5, pp 499-504

First online:

Stability theorems for Fourier frames and wavelet Riesz bases

  • Radu BalanAffiliated withProgram in Applied and Computational Mathematics, Princeton University

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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.

Math Subject Classifications

Primary 42C15 Secondary 41A30

Keywords and Phrases

Frames Riesz basis nonharmonic series wavelets