Geodesic
Nonstandard Representations of Locally Compact Groups
Matematičeskie zametki, Tome 82 (2007) no. 3, pp. 383-389 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the note, it is proved that, under natural conditions, any infinite-dimensional unitary representation $T$ of a direct product of groups $G=K\times N$, where $K$ is a compact group and $N$ is a locally compact Abelian group, is imaged by a representation of the nonstandard analog $\widetilde G$ of the group $G$ in the group of nonstandard matrices of a fixed nonstandard size.
Keywords: unitary representation, nonstandard matrix, imaging of groups, Boolean algebra, Stone space, Casimir operator. 
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V. A. Lyubetskii; S. A. Pirogov. Nonstandard Representations of Locally Compact Groups. Matematičeskie zametki, Tome 82 (2007) no. 3, pp. 383-389. http://geodesic.mathdoc.fr/item/MZM_2007_82_3_a5/

[1] P. S. Novikov, “O neprotivorechivosti nekotorykh polozhenii deskriptivnoi teorii mnozhestv”, Sbornik statei: Posv. akad. I. M. Vinogradovu k ego 60-letiyu, Tr. MIAN, 38, Nauka, M., 1951, 279–316 | MR | Zbl

[2] V. A. Lyubetskii, “Otsenki i puchki. O nekotorykh voprosakh nestandartnogo analiza”, UMN, 44:4 (1989), 99–153 | MR | Zbl

[3] T. Iekh, Teoriya mnozhestv i metod forsinga, Mir, M., 1973 | MR | Zbl

[4] E. I. Gordon, V. A. Lyubetskii, Bulevoznachnye rasshireniya ravnomernykh struktur I, dep. v VINITI 711-80

[5] V. A. Lyubetskii, E. I. Gordon, “Bulevy rasshireniya ravnomernykh struktur.”, Issledovaniya po neklassicheskim logikam i formalnym sistemam, Nauka, M., 1983, 81–153 | MR

[6] V. G. Kanovei, V. A. Lyubetskii, “O nekotorykh klassicheskikh problemakh deskriptivnoi teorii mnozhestv”, UMN, 58:5 (2003), 3–88 | MR | Zbl

[7] M. V. Terentev, Vvedenie v teoriyu elementarnykh chastits, ITEF, M., 1998

[8] D. A. Vladimirov, Bulevy algebry, Nauka, M., 1969 | MR | Zbl

[9] L. S. Pontryagin, Nepreryvnye gruppy, GITTL, M., 1954 | MR | Zbl

[10] M. A. Evgrafov, Analiticheskie funktsii, Nauka, M., 1968 | MR | Zbl

[11] M. A. Naimark, Normirovannye koltsa, Nauka, M., 1968 | MR | Zbl

[12] J. Dixmier, Les algèbras d'opérateurs dans l'espace Hilbertien (algèbres de von Neumann), Gauthier-Villars, Paris, 1969 | MR | Zbl