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

Alexander Ulanovskii; Ilya Zlotnikov

doi:10.1007/s00208-024-03011-7

Titel

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

Autor*in

Alexander Ulanovskii

Department of Mathematics and Physics, University of Stavanger

Ilya Zlotnikov

Fakultät für Mathematik, Universität Wien

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, new sharp results are obtained on the density of semi-regular lattices for the Gabor frames generated by elements from these families.

Objekt-Typ

journal article

Sprache

Englisch [eng]

Persistent identifier

https://phaidra.univie.ac.at/o:2101347

DOI

10.1007/s00208-024-03011-7

Erschienen in

Titel

Mathematische Annalen

ISSN