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

Elona Agora,Jorge Antezana,Carlos Cabrelli

doi:10.1016/j.aim.2015.08.006

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

Elona Agora, Jorge Antezana + Show 1 more

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https://doi.org/10.1016/j.aim.2015.08.006

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Journal: Advances in Mathematics	Publication Date: Aug 28, 2015
Citations: 38	License type: publisher-specific-oa

Affiliation: Instituto Argentino de Radioastronomía, Consejo Nacional de Investigaciones Científicas y Técnicas, Universidad Nacional de La Plata, University of Buenos Aires, Institute of Astronomy and Space Physics

#Locally Compact Abelian Groups #Locally Compact Abelian + Show 8 more

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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 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 Gˆ 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.

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