Gabor expansions and restricted summability

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Abstract

A general summability method, the so called θ-summability is considered for Gabor series. It is proved that the maximal operator of the θ-means defined in a cone is bounded from the local Hardy space h p to L p and from the amalgam space W (h p, ℓ ) to W (L p, ℓ∞). This implies the almost everywhere convergence of the θ-means for all f ∈ W (L 1, ℓ ).

Original languageEnglish
Pages (from-to)255-284
Number of pages30
JournalSampling Theory in Signal and Image Processing
Volume10
Issue number3
Publication statusPublished - Dec 1 2011

Keywords

  • Atomic decomposition
  • Gabor expansions
  • Gabor frames
  • Local hardy spaces
  • Time-frequency analysis
  • Wiener amalgam spaces
  • θ-summability

ASJC Scopus subject areas

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

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