Reducible representations of abelian groups

[Représentations réductibles des groupes abéliens]

Atzmon, Aharon

Annales de l'Institut Fourier, Tome 51 (2001), p. 1407-1418 / Harvested from Numdam

Résumé

Nous établissons un critère de réductibilité pour certaines représentations des groupes abéliens. Parmi les applications de ce critère, nous donnons une réponse positive au problème du sous-espace invariant par translation pour les espaces $L^p$ pondérés sur les groupes abéliens localement compacts, lorsque les poids sont pairs et $1<p<\infty $.

Abstract

A criterion for reducibility of certain representations of abelian groups is established. Among the applications of this criterion, we give a positive answer to the translation invariant subspace problem for weighted $L^p$ spaces on locally compact abelian groups, for even weights and $1<p<\infty $.

Détail

Publié le : 2001-01-01

MR 1860670 | Zbl 0980.43005

DOI : https://doi.org/10.5802/aif.1859
Classification:  43A65,  43A15,  47A15,  47B37
Mots clés: groupes abéliens, représentations réductibles, sous-espaces invariants par translation

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