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

Autor:	Ulanovskii, Alexander, Zlotnikov, Ilya
Rok vydání:	2024
Předmět:	Mathematics - Functional Analysis Mathematics - Classical Analysis and ODEs Mathematics - Complex Variables 42C15 42C40 94A20
Zdroj:	Mathematische Annalen (2024)
Druh dokumentu:	Working Paper
DOI:	10.1007/s00208-024-03011-7
Popis:	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. Comment: 27 pages, 1 figure, references added
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2402.03090 Zobrazit plný text záznamu View this record from Arxiv