Summability properties of Gabor expansions

Anton Baranov, Yurii Belov, Alexander Borichev

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We show that there exist complete and minimal systems of time-frequency shifts of Gaussians in L2(R) which are not strong Markushevich basis (do not admit the spectral synthesis). In particular, it implies that there is no linear summation method for general Gaussian Gabor expansions. On the other hand we prove that the spectral synthesis for such Gabor systems holds up to one dimensional defect.

Original languageEnglish
Pages (from-to)2532-2552
Number of pages21
JournalJournal of Functional Analysis
Volume274
Issue number9
DOIs
StatePublished - 1 May 2018

Scopus subject areas

  • Analysis

Keywords

  • Complete and minimal systems
  • Fock spaces
  • Gabor systems
  • Spectral synthesis
  • INTERPOLATION
  • DENSITY THEOREMS
  • BARGMANN-FOCK SPACE

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