Unitary representations of the infinite-dimensional classical groups $U(p,\infty)$, $SO_0(p,\infty)$, $Sp(p,\infty)$ and the corresponding motion groups
Funkcionalʹnyj analiz i ego priloženiâ, Tome 12 (1978) no. 3, pp. 32-44.

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     title = {Unitary representations of the infinite-dimensional classical groups $U(p,\infty)$, $SO_0(p,\infty)$, $Sp(p,\infty)$ and the corresponding motion groups},
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G. I. Olshanskii. Unitary representations of the infinite-dimensional classical groups $U(p,\infty)$, $SO_0(p,\infty)$, $Sp(p,\infty)$ and the corresponding motion groups. Funkcionalʹnyj analiz i ego priloženiâ, Tome 12 (1978) no. 3, pp. 32-44. http://geodesic.mathdoc.fr/item/FAA_1978_12_3_a3/

[1] Kirillov A.A., “Predstavleniya beskonechnomernoi unitarnoi gruppy”, DAN SSSR, 212:2 (1973), 288–290 | MR | Zbl

[2] Nelson E., “Analytic vectors”, Ann. Math., 70:3 (1959), 572–615 | DOI | MR | Zbl

[3] Olshanskii G.I., “Unitarnye predstavleniya beskonechnomernykh klassicheskikh grupp $U(p,\infty)$, $SO_0(p,\infty)$, $S_p(p,\infty)$ i sootvetstvuyuschikh grupp dvizhenii”, DAN SSSR, 238:6 (1978), 1295–1298 | MR

[4] Dedonne Zh., Keroll Dzh., Mamford D., Geometricheskaya teoriya invariantov, Mir, M., 1974 | MR

[5] Godement R., “Theory of spherical functions. I”, Trans. Amer. Math. Soc., 73, no. 3, 1952, 496–556 | DOI | MR | Zbl

[6] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, v. I, II, Nauka, M., 1973 ; 1974 | MR

[7] Diksme Zh., $\mathbf C^*$-algebry i ikh predstavleniya, Nauka, M., 1974 | MR

[8] Felps R., Lektsii o teoremakh Shoke, Mir, M., 1968

[9] Zhelobenko D.P., Kompaktnye gruppy Li i ikh predstavleniya, Nauka, M., 1970 | MR | Zbl

[10] Lepowsky J., “Algebraic results on representations of semisimple Lie groups”, Trans. Amer. Math. Soc., 176, 1973, 1–44 | DOI | MR | Zbl

[11] Berezin F.A., “Kvantovanie v kompleksnykh simmetricheskikh prostranstvakh”, Izv. AN SSSR, seriya matem., 39 (1975), 363–402 | MR | Zbl

[12] Molchanov V.F., “Predstavleniya psevdoortogonalnoi gruppy, svyazannye s konusom”, Matem. sb., 81 (1970), 358–375 | Zbl

[13] Yamasaki Y., “Projective limit of Haar measures on $O(n)$”, Publ. RIMS, Kyoto Univ., 8:1 (1972/73), 141–149 | DOI | MR | Zbl

[14] Krein M.G., “Ermitovo-polozhitelnye yadra na odnorodnykh prostranstvakh. I”, Ukr. matem. zh., 1:4 (1949), 64–98 | MR

[15] Schoenberg I.J., “Metric spaces and completely motonone functions”, Ann. Math., 39:4 (1938), 811–841 | DOI | MR

[16] Orihara A., “Hermite polynomials and infinite dimensional motion group”, J. Math. Kyoto Univ., 6:1 (1966), 1–12 | MR | Zbl

[17] Ismagilov R.C., “O lineinykh predstavleniyakh grupp matrits s elementami iz normirovannogo polya”, Izv. AN SSSR, seriya matem., 33 (1969), 1296–1323 | MR | Zbl

[18] Nikolov A.V., Rerikh K.V., Diskretnaya seriya unitarnykh predstavlenii algebry Li gruppy $U(p,q)$, preprint OIYaI, 5-2962, Dubna, 1966 | MR

[19] Mickelsson J., Niederle J., “On integrability of discrete representations of Lie algebras $U(p,q)$”, Ann. Inst. H. Poincaré, ser. A., 19:1 (1973), 171–177 | MR

[20] Nikolov A.V., “Ob odnoi vyrozhdennoi serii unitarnykh predstavlenii algebry Li gruppy $O(p,q)$”, Funkts. analiz, 3:4 (1969), 91–92 | MR | Zbl