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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 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.

Registro:

Documento: Artículo
Título:Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups
Autor:Agora, E.; Antezana, J.; Cabrelli, C.
Filiación:Instituto Argentino de Matemática Alberto P. Calderón (IAM-CONICET), Argentina
Departamento de Matemática, Universidad Nacional de La Plata, Argentina
Departamento de Matemática, Universidad de Buenos Aires, Argentina
Instituto de Matemática Luis Santaló (IMAS-CONICET-UBA), Argentina
Palabras clave:Beurling's densities; Dyadic cubes; Interpolation; Locally compact abelian groups; Multi-tiling; Riesz bases; Sampling
Año:2015
Volumen:285
Página de inicio:454
Página de fin:477
DOI: http://dx.doi.org/10.1016/j.aim.2015.08.006
Título revista:Advances in Mathematics
Título revista abreviado:Adv. Math.
ISSN:00018708
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v285_n_p454_Agora

Referencias:

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  • Grepstad, S., Lev, N., Multi-tiling and Riesz bases (2014) Adv. Math., 252, pp. 1-6
  • Gröchenig, K., Kutyniok, G., Seip, K., Landau's necessary density conditions for LCA groups (2008) J. Funct. Anal., 255 (7), pp. 1831-1850
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  • Marzo, J., Riesz basis of exponentials for a union of cubes in Rd, , arxiv:math/0601288, preprint
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  • Seip, K., Interpolation and Sampling in Spaces of Analytic Functions (2004) University Lecture Series, 33. , American Mathematical Society, Providence, RI, xii+139 pp

Citas:

---------- APA ----------
Agora, E., Antezana, J. & Cabrelli, C. (2015) . Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups. Advances in Mathematics, 285, 454-477.
http://dx.doi.org/10.1016/j.aim.2015.08.006
---------- CHICAGO ----------
Agora, E., Antezana, J., Cabrelli, C. "Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups" . Advances in Mathematics 285 (2015) : 454-477.
http://dx.doi.org/10.1016/j.aim.2015.08.006
---------- MLA ----------
Agora, E., Antezana, J., Cabrelli, C. "Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups" . Advances in Mathematics, vol. 285, 2015, pp. 454-477.
http://dx.doi.org/10.1016/j.aim.2015.08.006
---------- VANCOUVER ----------
Agora, E., Antezana, J., Cabrelli, C. Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups. Adv. Math. 2015;285:454-477.
http://dx.doi.org/10.1016/j.aim.2015.08.006