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

Title

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

Author

Alexander Ulanovskii

Department of Mathematics and Physics, University of Stavanger

Ilya Zlotnikov

Faculty of Mathematics, University of Vienna

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.

Object type

journal article

Language

English [eng]

Persistent identifier

phaidra.univie.ac.at/o:2101347

DOI

10.1007/s00208-024-03011-7

Appeared in

Title

Mathematische Annalen

ISSN