Gabor analysis on Wiener amalgams

Hans G. Feichtinger, Ferenc Weisz

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

A general summability method, the so-called θ-summability, is considered for Gabor series. Under suitable conditions on θ we prove that this summation method of the Gabor expansion of f converges to f in Wiener amalgam norms, and in particular with respect to Lp-norms, for functions f from the corresponding spaces, as well as almost everywhere. Some inequalities for the maximal operator of the θ-means of the Gabor expansion are obtained. The analogous statements for the partial sums of Gabor series are also given. The classical Hardy-Littlewood inequality and the Marcinkiewicz multiplier theorem is shown to be valid in the context of Gabor series.

Original languageEnglish
Pages (from-to)129-150
Number of pages22
JournalSampling Theory in Signal and Image Processing
Volume6
Issue number2
Publication statusPublished - May 1 2007

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Keywords

  • Gabor expansions
  • Gabor frames
  • Hardy-Littlewood inequality
  • Herz space
  • Multipliers
  • Time-frequency analysis
  • Walnut representation
  • Weiner amalgam spaces
  • θ-summability

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Radiology Nuclear Medicine and imaging
  • Computational Mathematics

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