Linear approximation and reproduction of polynomials by Wilson bases

Kai Bittner

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


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
Issue number1
Publication statusPublished - 2002
Externally publishedYes


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


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