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

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 (2008) [7]. To achieve this result, we prove the existence of universal Riesz bases...

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Detalles Bibliográficos
Autores principales: Agora, E., Antezana, J., Cabrelli, C.
Formato: JOUR
Materias:
Beurling's densities
Dyadic cubes
Interpolation
Locally compact abelian groups
Multi-tiling
Riesz bases
Sampling
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00018708_v285_n_p454_Agora
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario: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 (2008) [7]. 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 Ĝ 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. © 2015 Elsevier Inc.

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