[Sous-pavages en réseau et trames dans les groupes abéliens, localement compacts]
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.
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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@article{CRMATH_2017__355_2_193_0,
author = {Barbieri, Davide and Hern\'andez, Eugenio and Mayeli, Azita},
title = {Lattice sub-tilings and frames in {LCA} groups},
journal = {Comptes Rendus. Math\'ematique},
pages = {193--199},
publisher = {Elsevier},
volume = {355},
number = {2},
year = {2017},
doi = {10.1016/j.crma.2016.11.017},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2016.11.017/}
}
TY - JOUR AU - Barbieri, Davide AU - Hernández, Eugenio AU - Mayeli, Azita TI - Lattice sub-tilings and frames in LCA groups JO - Comptes Rendus. Mathématique PY - 2017 SP - 193 EP - 199 VL - 355 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2016.11.017/ DO - 10.1016/j.crma.2016.11.017 LA - en ID - CRMATH_2017__355_2_193_0 ER -
%0 Journal Article %A Barbieri, Davide %A Hernández, Eugenio %A Mayeli, Azita %T Lattice sub-tilings and frames in LCA groups %J Comptes Rendus. Mathématique %D 2017 %P 193-199 %V 355 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2016.11.017/ %R 10.1016/j.crma.2016.11.017 %G en %F CRMATH_2017__355_2_193_0
Barbieri, Davide; Hernández, Eugenio; Mayeli, Azita. Lattice sub-tilings and frames in LCA groups. Comptes Rendus. Mathématique, Tome 355 (2017) no. 2, pp. 193-199. doi : 10.1016/j.crma.2016.11.017. http://www.numdam.org/articles/10.1016/j.crma.2016.11.017/
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