Reducible representations of abelian groups

Atzmon, Aharon

Annales de l'Institut Fourier, Tome 51 (2001) no. 5, pp. 1407-1418.

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 $1<p<\infty$.

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 $1<p<\infty$.

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