Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups
Classical Analysis and ODEs
2015-08-11 v4 Functional Analysis
Abstract
We prove the existence of sampling sets and interpolation sets near the critical density, in Paley Wiener spaces of a locally compact abelian (LCA) group G . This solves a problem left by Gr\"ochenig, Kutyniok, and Seip in the article: `Landau's density conditions for LCA groups ' (J. of Funct. Anal. 255 (2008) 1831-1850). To achieve this result, we prove the existence of universal Riesz bases of characters for L2(Omega), provided that the relatively compact subset Omega of the dual group of G satisfies a multi-tiling condition. This last result generalizes Fuglede's theorem, and extends to LCA groups setting recent constructions of Riesz bases of exponentials in bounded sets of Rd.
Keywords
Cite
@article{arxiv.1404.2317,
title = {Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups},
author = {Elona Agora and Jorge Antezana and Carlos Cabrelli},
journal= {arXiv preprint arXiv:1404.2317},
year = {2015}
}
Comments
21 pages, 1 figure