Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups

AGORA, ELONA; ANTEZANA, JORGE; CABRELLI, CARLOS

ADVANCES IN MATHEMATICS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2015 vol. 285 p. 454 - 477

0001-8708

We prove the existence of sampling sets and interpolationsets near the critical density, in Paley Wiener spaces of alocally compact abelian (LCA) group G. This solves a problemleft by Gröchenig, Kutyniok, and Seip (2008) [7]. To achievethis result, we prove the existence of universal Riesz basesof characters for L2(Ω), provided that the relatively compactsubset Ω of the dual group G satisfies a multi-tiling condition.This last result generalizes Fuglede?s theorem, and extendsto LCA groups setting recent constructions of Riesz bases ofexponentials in bounded sets of Rd.