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Perturbation of wavelet and Gabor frames

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Analysis in Theory and Applications

Abstract

In this work two aspects of theory of frames are presented: a side necessary condition on irregular wavelet frames is obtained, another perturbation of wavelet and Gabor frames is considered. Specifically, we present the results obtained on frame stability when one disturbs the mother of wavelet frame, or the parameter of dilatation, and in Gabor frames when the generating function or the parameter of translation are perturbed. In all cases we work without demanding compactness of the support, neither on the generating function, nor on its Fourier transform.

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Authors and Affiliations

  1. Instituto de Matemática Aplicada San Luis, Universidad Nacional de San Luis, Av. Ejército de Los Andes 950.5700, San Luis, Argentina

    Ivana Carrizo & Sergio Favier

Authors
  1. Ivana Carrizo
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  2. Sergio Favier
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Correspondence to Ivana Carrizo.

Additional information

This work was supported by CONICET and Universidad Nacional de San Luis.

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Carrizo, I., Favier, S. Perturbation of wavelet and Gabor frames. Anal. Theory Appl. 19, 238–254 (2003). https://doi.org/10.1007/BF02835283

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  • DOI: https://doi.org/10.1007/BF02835283

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