Lattice sub-tilings and frames in LCA groups

Davide Barbieri; Eugenio Hernández; Azita Mayeli

doi:10.1016/j.crma.2016.11.017

Harmonic analysis/Theory of signals

Lattice sub-tilings and frames in LCA groups
[Sous-pavages en réseau et trames dans les groupes abéliens, localement compacts]

Présenté par : the Editorial Board

Davide Barbieri ¹ ; Eugenio Hernández ¹ ; Azita Mayeli ²

¹ Universidad Autónoma de Madrid, 28049 Madrid, Spain
² City University of New York, Queensborough and the Graduate Center, New York, USA

Comptes Rendus. Mathématique, Volume 355 (2017) no. 2, pp. 193-199.

Résumé
Abstract

Soit Λ un réseau. On prouve que les caractères de G associés au réseau dual forment une trame de $L^{2} (Ω)$ si et seulement si les différents translatés de Ω par Λ sont d'intersection presque vide. Ceci entraîne le théorème bien connu de Fuglede pour les réseaux, ainsi qu'une caractérisation simple des trames de modulation.

Given a lattice Λ in a locally compact Abelian group G and a measurable subset Ω with finite and positive measure, then the set of characters associated with the dual lattice form a frame for $L^{2} (Ω)$ if and only if the distinct translates by Λ of Ω have almost empty intersections. Some consequences of this results are the well-known Fuglede theorem for lattices, as well as a simple characterization for frames of modulates.

Reçu le : 2016-10-01
Accepté le : 2016-11-30
Publié le : 2016-12-21

DOI : 10.1016/j.crma.2016.11.017

Affiliations des auteurs :

Davide Barbieri ¹ ; Eugenio Hernández ¹ ; Azita Mayeli ²

¹ Universidad Autónoma de Madrid, 28049 Madrid, Spain
² City University of New York, Queensborough and the Graduate Center, New York, USA

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     title = {Lattice sub-tilings and frames in {LCA} groups},
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     pages = {193--199},
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     language = {en},
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Davide Barbieri; Eugenio Hernández; Azita Mayeli. Lattice sub-tilings and frames in LCA groups. Comptes Rendus. Mathématique, Volume 355 (2017) no. 2, pp. 193-199. doi : 10.1016/j.crma.2016.11.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.11.017/

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