Sampling in quasi shift-invariant spaces and Gabor frames generated by ratios of exponential polynomials: On Gabor frames generated by ratios of exponential polynomials

Alexander Ulanovskii, Ilia Zlotnikov

Veröffentlichungen: Working PaperPreprint

Abstract

We introduce two families of generators (functions) $G$ that consist of entire and meromorphic functions enjoying a certain periodicity property and contain the classical Gaussian and hyperbolic secant generators. Sharp results are proved on the density of separated sets that provide non-uniform sampling for the shift-invariant and quasi shift-invariant spaces generated by elements of these families.
As an application, we obtain new sharp results on the density of semi-regular lattices for the Gabor frames generated by elements from these families.
OriginalspracheEnglisch
Seitenumfang26
DOIs
PublikationsstatusVeröffentlicht - 6 Feb. 2024

ÖFOS 2012

  • 101002 Analysis
  • 101008 Funktionentheorie
  • 101032 Funktionalanalysis
  • 101031 Approximationstheorie

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