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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Ulanovskii, Alexander, Zlotnikov, Ilya
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866910848752025600
author Ulanovskii, Alexander
Zlotnikov, Ilya
author_facet Ulanovskii, Alexander
Zlotnikov, Ilya
contents We introduce two families of generators (functions) $\mathcal{G}$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2402_03090
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Sampling in quasi shift-invariant spaces and Gabor frames generated by ratios of exponential polynomials
Ulanovskii, Alexander
Zlotnikov, Ilya
Functional Analysis
Classical Analysis and ODEs
Complex Variables
42C15, 42C40, 94A20
We introduce two families of generators (functions) $\mathcal{G}$ 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.
title Sampling in quasi shift-invariant spaces and Gabor frames generated by ratios of exponential polynomials
topic Functional Analysis
Classical Analysis and ODEs
Complex Variables
42C15, 42C40, 94A20
url https://arxiv.org/abs/2402.03090