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Discrete Fourier-Jacobi Transform and Generalized Lipschitz Classes

Acta Mathematica Vietnamica (2022)Cite this article

Abstract

In this paper, we use the methods of Fourier-Jacobi harmonic analysis to generalize Boas-type results. We give necessary and sufficient conditions in terms of the Fourier-Jacobi coefficients of a function f in order to ensure that it belongs either to one of the generalized Lipschitz classes \({H}_{\alpha }^{m}\) and \({h}_{\alpha }^{m}\) for α > 0.

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Authors and Affiliations

  1. Chouaib Doukkali University of El Jadida, Natl Sch Appl Sci, Sci Engineer Lab Energy, El Jadida, Morocco

    El Mehdi Loualid

  2. Laboratory Mathematics and Informatics, Faculty of Sciences Aïn Chock, University of Hassan II, B.P 5366, Maarif, Casablanca, Morocco

    El Mehdi Loualid, Abdelghani Elgargati & Radouan Daher

Authors
  1. El Mehdi Loualid
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  2. Abdelghani Elgargati
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  3. Radouan Daher
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Correspondence to El Mehdi Loualid.

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Loualid, E.M., Elgargati, A. & Daher, R. Discrete Fourier-Jacobi Transform and Generalized Lipschitz Classes. Acta Math Vietnam (2022). https://doi.org/10.1007/s40306-022-00478-x

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  • DOI: https://doi.org/10.1007/s40306-022-00478-x

Keywords

  • Discrete Fourier-Jacobi transform
  • Boas-type theorems
  • Generalized Lipschitz classes
  • Generalized Zygmund classes

Mathematics Subject Classification (2010)

  • 42B35
  • 42A38
  • 26A16
  • 42A16