Comptes Rendus
no. 2
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 Barbieri1 ; Eugenio Hernández1 ; Azita Mayeli2
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.

Soit Λ un réseau. On prouve que les caractères de G associés au réseau dual forment une trame de L2(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 L2(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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.11.017
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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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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