Geodesic
Invariant subspaces of some function spaces on symmetric spaces.~I
Izvestiya. Mathematics , Tome 59 (1995) no. 5, pp. 1007-1050.

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The article describes the construction of closed linear subspaces of some function spaces on the symmetric space $M=\operatorname{SU}(n,1)/U(n)$ that are invariant with respect to the natural quasiregular representation of the group $\operatorname{SU}(n,1)$. The function spaces considered include, in particular, the spaces $C^d(M)$ $(d=0,1,\dots,\infty)$ and spaces of functions of exponential growth on $M$. 
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S. S. Platonov. Invariant subspaces of some function spaces on symmetric spaces.~I. Izvestiya. Mathematics , Tome 59 (1995) no. 5, pp. 1007-1050. http://geodesic.mathdoc.fr/item/IM2_1995_59_5_a8/

[1] Schwartz L., “Theorie générale des fonctions moyenneperiodique”, Ann. Math., 48 (1947), 875–929 | DOI | MR

[2] Gurevich D. I., “Kontrprimery k gipoteze Shvartsa”, Funkts. analiz i ego prilozh., 9:2 (1975), 29–35 | MR | Zbl

[3] Ehrenpreis L., Maytner F. J., “Some properties of the Fourier transform on the semisimple Lie groups, III”, Trans. Amer. Math. Soc., 90 (1959), 431–484 | DOI | MR | Zbl

[4] Rashevskii P. K., “Opisanie invariantnykh podprostranstv v nekotorykh funktsionalnykh prostranstvakh”, Tr. MMO, 38, URSS, M., 1979, 139–185 | MR

[5] Berenstein C. A., “Spectral synthesis on symmetric spaces”, Contemp. Math., 63 (1987), 1–25 | MR | Zbl

[6] Berenstein C. A., Gay R., “Sur la synthése spectrale dans les espaces symmetriques”, J. Math. Pure et Appl., 65 (1986), 323–334 | MR

[7] Wawrzynczyk A., “Spectral analisis and synthesis on symmetric spaces”, J. Math. Ann. and Appl., 127 (1987), 1–17 | DOI | MR | Zbl

[8] Khelgason S., Differentsialnaya geometriya i simmetricheskie prostranstva, Mir, M., 1964 | Zbl

[9] Robertson A., Robertson B., Topologicheskie vektornye prostranstva, Mir, M., 1967 | MR | Zbl

[10] Platonov S. S., “Invariantnye podprostranstva v nekotorykh funktsionalnykh prostranstvakh na $n$-mernom prostranstve Lobachevskogo”, Matem. sb., 137:12 (1988), 435–461 | Zbl

[11] Platonov S. S., “O spektralnom sinteze na simmetricheskikh prostranstvakh ranga 1”, Algebra i analiz, 4:4 (1992), 174–187 | MR | Zbl

[12] Platonov S. S., “Invariantnye podprostranstva v nekotorykh funktsionalnykh prostranstvakh na gruppe $\operatorname {SL}(2,\mathbb C)$”, Tr. sem. po vekt. i tenz. anal., no. 21, 1983, 191–258 | MR | Zbl

[13] Helgason S., “A duality for symmetric spaces with applications to group representations, I”, Adv. Math., 5 (1970), 1–154 | DOI | MR | Zbl

[14] Platonov S. S., “Invariantnye podprostranstva v nekotorykh funktsionalnykh prostranstvakh na simmetricheskikh prostranstvakh ranga 1”, DAN SSSR, 303:4 (1988), 797–799 | MR | Zbl

[15] Platonov S. S., “Invariantnye podprostranstva v nekotorykh funktsionalnykh prostranstvakh na simmetricheskikh prostranstvakh ranga 1 (simplekticheskii i osobyi sluchai)”, DAN SSSR, 322:2 (1992), 243–247 | MR | Zbl

[16] Vladimirov V. S., Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1979 | MR

[17] Khelgason S., Gruppy i geometricheskii analiz, Mir, M., 1987 | MR

[18] Diksme Zh., Universalnye obertyvayuschie algebry, Mir, M., 1978 | MR

[19] Gisharde A., Kogomologii topologicheskikh grupp i algebr Li, Mir, M., 1984 | MR

[20] Zhelobenko D. P., Shtern A. I., Predstavleniya grupp Li, Nauka, M., 1983 | MR

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

[22] Kass N., “Explicit decompositions of some tensor products of modules for semisimple Lie algebras”, Commun. Algebra, 15 (1987), 2251–2261 | DOI | MR | Zbl

[23] Goto M., Groskhans F., Poluprostye algebry Li, Mir, M., 1981 | MR | Zbl

[24] Leng S., $SL_2(\mathbb R)$, Mir, M., 1977