Reducible representations of abelian groups
Annales de l'Institut Fourier, Volume 51 (2001) no. 5, p. 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 : https://doi.org/10.5802/aif.1859
Classification:  43A65,  43A15,  47A15,  47B37
Keywords: abelian groups, reducible representations, translation invariant subspaces
@article{AIF_2001__51_5_1407_0,
     author = {Atzmon, Aharon},
     title = {Reducible representations of abelian groups},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {51},
     number = {5},
     year = {2001},
     pages = {1407-1418},
     doi = {10.5802/aif.1859},
     mrnumber = {1860670},
     zbl = {0980.43005},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2001__51_5_1407_0}
}
Reducible representations of abelian groups. Annales de l'Institut Fourier, Volume 51 (2001) no. 5, pp. 1407-1418. doi : 10.5802/aif.1859. https://aif.centre-mersenne.org/item/AIF_2001__51_5_1407_0/

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