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Comptes Rendus Mathématique
Volume 355, n° 2
pages 193-199 (février 2017)
Doi : 10.1016/j.crma.2016.11.017
Received : 1 October 2016 ;  accepted : 30 November 2016
Lattice sub-tilings and frames in LCA groups
Sous-pavages en réseau et trames dans les groupes abéliens, localement compacts

Davide Barbieri a , Eugenio Hernández a , Azita Mayeli b
a Universidad Autónoma de Madrid, 28049 Madrid, Spain 
b City University of New York, Queensborough and the Graduate Center, New York, USA 


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   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.

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Soit Λ un réseau. On prouve que les caractères de G associés au réseau dual forment une trame de   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.

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