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

doi:10.48550/arXiv.2402.03090

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

Department of Mathematics

Publications: Working paper › Preprint

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.

Original language	English
Number of pages	26
DOIs	https://doi.org/10.48550/arXiv.2402.03090
Publication status	Published - 6 Feb 2024

Austrian Fields of Science 2012

101002 Analysis
101008 Complex analysis
101032 Functional analysis
101031 Approximation theory

Keywords

non-uniform sampling
EXPONENTIAL POLYNOMIALS
Quasi shift-invariant space
Gabor frame
Shift-invariant space

Access to Document

10.48550/arXiv.2402.03090Licence: CC BY 4.0

1 Active

Inside the Frame Set
Faulhuber, M.
1/03/21 → 28/02/25
Project: Research funding

2 Talk or oral contribution

Sampling theorems in (quasi) shift-invariant spaces generated by ratios of exponential polynomials(based on joint paper with A. Ulanovskii)
Ilia Zlotnikov (Speaker)
29 May 2024
Activity: Talks and presentations › Talk or oral contribution › Science to Science
New sharp sampling theorems in (quasi) shift-invariant spaces (based on joint papers with A. Ulanovskii and J.L. Romero)
Ilia Zlotnikov (Speaker)
11 Apr 2024
Activity: Talks and presentations › Talk or oral contribution › Science to Science

1 Article

Sampling in quasi shift-invariant spaces and Gabor frames generated by ratios of exponential polynomials
Ulanovskii, A. & Zlotnikov, I., 4 Oct 2024, In: Mathematische Annalen. 28 p.
Publications: Contribution to journal › Article › Peer Reviewed

Open Access

Cite this

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

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.",

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T2 - On Gabor frames generated by ratios of exponential polynomials

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Y1 - 2024/2/6

N2 - 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.

AB - 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.

KW - non-uniform sampling

KW - EXPONENTIAL POLYNOMIALS

KW - Quasi shift-invariant space

KW - Gabor frame

KW - Shift-invariant space

U2 - 10.48550/arXiv.2402.03090

DO - 10.48550/arXiv.2402.03090

M3 - Preprint

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

ER -

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

Abstract

Austrian Fields of Science 2012

Keywords

Access to Document

Fingerprint

Projects

Inside the Frame Set

Activities

Sampling theorems in (quasi) shift-invariant spaces generated by ratios of exponential polynomials(based on joint paper with A. Ulanovskii)

New sharp sampling theorems in (quasi) shift-invariant spaces (based on joint papers with A. Ulanovskii and J.L. Romero)

Research output

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

Cite this