Artículos de revistas
Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups
Fecha
2015-11Registro en:
Cabrelli, Carlos; Antezana, Jorge Abel; Agora, Elona; Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups; Academic Press Inc Elsevier Science; Advances In Mathematics; 285; 11-2015; 454-477
0001-8708
Autor
Cabrelli, Carlos
Antezana, Jorge Abel
Agora, Elona
Resumen
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 Gröchenig, Kutyniok, and Seip in 2008. To achieve this result, we prove the existence of universal Riesz bases of characters for L2(Ω), provided that the relatively compact subset Ω 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.