Reducible representations of abelian groups
Annales de l'Institut Fourier, Volume 51 (2001) no. 5, pp. 1407-1418.

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<.

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<.

DOI: 10.5802/aif.1859
Classification: 43A65, 43A15, 47A15, 47B37
Keywords: abelian groups, reducible representations, translation invariant subspaces
Mot clés : groupes abéliens, représentations réductibles, sous-espaces invariants par translation
Atzmon, Aharon 1

1 Tel Aviv University, School of Mathematical Sciences, Tel Aviv 69978 (Israël)
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Atzmon, Aharon. Reducible representations of abelian groups. Annales de l'Institut Fourier, Volume 51 (2001) no. 5, pp. 1407-1418. doi : 10.5802/aif.1859. http://archive.numdam.org/articles/10.5802/aif.1859/

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