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Results on Non-linear Approximation for Wavelet Bases in Weighted Function Spaces

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New Trends in Applied Harmonic Analysis

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

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Abstract

The material in this paper comes from various conferences given by the authors. We start with a brief survey of harmonic analysis methods in linear and non-linear approximation related to signal compression. Special emphasis is made on wavelet-based methods and some of the mathematical theory of wavelets behind them. We also present recent results of the authors concerning non-linear approximation in sequence spaces and the validity of Jackson and Bernstein inequalities in general smoothness spaces.

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Acknowledgements

The author “Eugenio Hernández” was supported by MINECO Grants MTM-2010-16518 and MTM-2013-40945-P. The author “Maria de Natividade” was supported by MCT-Angola and FCUAN-Angola.

Author information

Authors and Affiliations

  1. Departamento de Matemáticas, Módulo 17, Universidad Autónoma de Madrid, 28049, Madrid, Spain

    Eugenio Hernández

  2. Faculdade de Ciencias, Departamento de Matemática, Universidade Agostinho Neto, Avenida 4 de Fevereiro nro. 71, 1 andar e campus universitario da Camama, C.P. no. 825, Luanda, Angola

    Maria de Natividade

Authors
  1. Eugenio Hernández
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  2. Maria de Natividade
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Correspondence to Eugenio Hernández .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Vanderbilt University, Nashville, Tennessee, USA

    Akram Aldroubi

  2. Depto. de Matemática, Univ. de Buenos Ai, IMAS - UBA/CONICET, Buenos Aires, Argentina

    Carlos Cabrelli

  3. UFR de Sciences et Technologie, Universite Paris Est Creteil, Creteil Cedex, Paris, France

    Stephane Jaffard

  4. Depto. de Matemática, Univ. de Buenos Ai, IMAS, UBA/CONICET, Buenos Aires, Argentina

    Ursula Molter

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Hernández, E., de Natividade, M. (2016). Results on Non-linear Approximation for Wavelet Bases in Weighted Function Spaces. In: Aldroubi, A., Cabrelli, C., Jaffard, S., Molter, U. (eds) New Trends in Applied Harmonic Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-27873-5_5

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