On some Hermite series identities and their applications to Gabor analysis

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Abstract

We prove some infinite series identities for the Hermite functions. From these identities we disprove the Gabor frame set conjecture for Hermite functions of order (Formula presented.) and (Formula presented.) for (Formula presented.). The results hold not only for Hermite functions, but for two large classes of eigenfunctions of the Fourier transform associated with the eigenvalues (Formula presented.) and i, and the results indicate that the Gabor frame set of all such functions must have a rather complicated structure.
Original languageEnglish
JournalMonatshefte für Mathematik
Volume182
Issue number4
Pages (from-to)899–912
ISSN0026-9255
DOIs
Publication statusPublished - 2016

Keywords

  • Hermite functions
  • Frame
  • Frame set
  • Garbor system
  • Zak transform
  • Zibulski–Zeevi matrix

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