Linear approximation and reproduction of polynomials by Wilson bases

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Abstract

Wilson bases are constituted by trigonometric functions multiplied by translates of a window function with good time frequency localization. In this article we investigate the approximation of functions from Sobolev spaces by partial sums of the Wilson basis expansion. In particular, we show that the approximation can be improved if polynomials are reproduced. We give examples of Wilson bases, which reproduce linear functions with the lowest-frequency term only.

Original languageEnglish
Pages (from-to)85-108
Number of pages24
JournalJournal of Fourier Analysis and Applications
Volume8
Issue number1
DOIs
Publication statusPublished - 2002
Externally publishedYes

Keywords

  • Biorthogonality
  • Local trigonometric bases
  • Riesz basis
  • Unconditional bases
  • Wilson bases

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