Plancherel Formula for Berezin Deformation of L2 on Riemannian Symmetric Space

Elsevier BV - Tập 189 Số 2 - Trang 336-408 - 2002
Yurii A. Yurii A.

Tài liệu tham khảo

Anker, 2001, Heat kernel and Green function estimates on non-compact symmetric spaces. II, 28 Arazy, 1997, Invariant inner products in spaces of holomorphic functions on bounded symmetric domains, Documenta Math., 2, 213, 10.4171/dm/29 Arazy, 1995, Invariant mean value and harmonicity in Cartan and Siegel domains, 175 Berezin, 1975, Quantization in complex symmetric domains, Izv. Akad. Nauk SSSR Ser. Mat., 9, 1362 Berezin, 1978, On relations between covariant and contravariant symbols of operators for complex classical domains, Dokl. Akad Nauk SSSR, 241 Berezin, 1958, Zonal spherical functions and Laplace operators on some symmetric spaces, Dokl. Akad. Nauk SSSR, 118, 9 Bergmann, 1947 van Dijk, 1997, Canonical representations related to hyperbolic spaces, J. Funct. Anal., 147, 109, 10.1006/jfan.1996.3057 van Dijk, 1999, The Berezin form for rank 1 para-hermitian symmetric spaces, J. Math. Pures. Appl. (9), 78, 99, 10.1016/S0021-7824(99)80011-7 Faraut, 1994 Gantmakher, 1988 Gindikin, 1964, Analysis on homogeneous spaces, Usp. Mat. Nauk., 19, 3 Gindikin, 1975, Invariant distributions in homogeneous domains, Funktsional. Anal. i Prilozhen., 9, 56, 10.1007/BF01078179 Gindikin, 1962, Plancherel measure for Riemannian symmetric spaces of non-positive curvature, Dokl. Akad. Nauk SSSR, 145, 252 Gindikin, 1966, On an integral connected with symmetric Riemannian space of non-positive curvature, Izv. Akad. Nauk SSSR Ser. Mat., 30, 1147 Gutkin, 1979, Coefficients of Clebsch–Gordon for holomorphic discrete series, Lett. Math. Phys., 3, 185, 10.1007/BF00405291 Heckman, 1987, Root systems and hypergeometric functions, Compos. Math., 64, 329 Helgason, 1984 Hille, 1999 1953 Hoogenboom, 1982, Spherical functions and invariant differential operators on complex Grassmann manifolds, Ark. Mat., 20, 58, 10.1007/BF02390499 Hua, 1958 Jaffee, 1975, Real forms of hermitian symmetric spaces, Bull. Amer. Math. Soc., 81, 456, 10.1090/S0002-9904-1975-13783-9 Kirillov, 1972 Knapp, 1986 Kobayashi, 1992, Singular unitary representations and indefinite Stiefel manifolds, Mem. Amer. Math. Soc., 95 Krein, 1949, Hermitian positive definite kernels on homogeneous spaces, I, II, Ukr. Math. J., 1, 64 Molchanov, 1980, Tensor products for unitary representations of three-dimensional Lorentz group, Math. USSR Izv., 15, 113, 10.1070/IM1980v015n01ABEH001191 A. I. Molev, Unitarizability of some Enright–Varadarajan U(p, q)-modules, in Topics in Representation Theory (A. A. Kirillov, Ed.), Adv. Soc. Math., Vol. 2, pp. 199–220, Amer. Math. Soc. Transl. Nagano, 1965, Transformation groups on compact symmetric spaces, Trans. Amer. Math. Soc., 118, 428, 10.1090/S0002-9947-1965-0182937-8 Neretin, 1986, On discrete occurrence of complementary series representations in tensor products of unitary representations, Funct. Anal. Appl., 20, 79, 10.1007/BF01077323 Neretin, 1991, Extension of representations of classical groups to representations of categories, Algebra i Analiz, 3, 176 Neretin, 1996 Neretin, 1998, Boundary values of holomorphic functions and some spectral problems for unitary representations Neretin, 1998, Restriction of a function holomorphic in a domain to a curves lying on the boundary and discrete SL2(R)-spectra, Izv. Ross. Akad. Nauk Ser. Mat., 62, 67 Neretin, 2000, Matrix analogues of the B-function, and the Plancherel formula for Berezin kernel representations, Mat. Sb., 191, 67 Neretin, 2000, On the separation of spectra in the analysis of Berezin kernels, Funktsional. Anal. i Prilozhen., 34, 49, 10.1007/BF02482409 Neretin, 1999, Conformal geometry of symmetric spaces and Krein–Shmulyan functor, Mat. Sb., 10.1070/SM1999v190n02ABEH000385 Neretin, 2001, Index hypergeometric transform and an imitation of the analysis of Berezin kernels on hyperbolic spaces, Mat. Sb., 192, 83 Yu. A. Neretin, Matrix balls, radial analysis of Berezin kernels, and hypergeometric determinants, Moscow Math. J.1, No. , 157–220, preprint, available at http://xxx.lanl/gov/RT/0012220. Neretin, 1995, Boundary values of holomorphic functions, singular unitary representations of groups O(p, q) and their limits as q→∞, Zap. Nauchn. Sem. S.-Petersburg. Otdel. Mat. Inst. Steklov., 223, 9 Olafsson, 1996, Bargmann transform for symmetric spaces, 3 Ørsted, 1997, Tensor products of analytic continuations of discrete series, Can. J. Math., 49, 1224, 10.4153/CJM-1997-060-5 Olshanskii, 1982, Convex cones in symmetric Lie algebras, Lie semigroups and invariant causal (order) structures on pseudoriemannian symmetric spaces, Dokl. Acad. Nauk SSSR, 265, 537 Olshanskii, 1982, Invariant cones in Lie algebra, Lie semigroups and holomorphic discrete series, Funct. Anal. Appl., 15, 275, 10.1007/BF01106156 Olshanskii, 1989, Irreducible unitary representations of the groups U(p, q) which admits the pass to the limit as q→∞, Zap. Nauchn. Sem. Leningrad Otdel. Mat. Inst., 172, 114 Piatecki-Shapiro, 1961 Pickrell, 1987, Measures on infinite-dimensional Grassmann manifolds, J. Funct. Anal., 70, 323, 10.1016/0022-1236(87)90116-9 Pukanszky, 1961, On the Kronecker products of irreducible representations of 2×2 real unimodular group, Trans. Amer. Math. Soc., 100, 116, 10.2307/1993356 Repka, 1979, Tensor products of holomorphic discrete series, Can. J Math., 31, 836, 10.4153/CJM-1979-079-9 Rossi, 1976, Analytic continuations of holomorphic discrete series of semisimple Lie groups, Acta Math., 136, 1, 10.1007/BF02392042 Siegel, 1935, Uber die analytische Theorie der quadratischen Formen, Ann. Math., 36, 527, 10.2307/1968644 Shimeno, 1994, The Plancherel formula for spherical functions with a one-dimensional K-type on a simply connected simple Lie group of Hermitian type, J. Funct. Anal., 121, 330, 10.1006/jfan.1994.1052 Schlichtkrull, 1982, A series of unitary irreducible representations induced from the symmetric subgroup of semisimple Lie group, Invent. Math., 68, 497, 10.1007/BF01389414 Schoenberg, 1938, Metric spaces and positive definite functions, Trans. Amer. Math. Soc., 44, 522, 10.1090/S0002-9947-1938-1501980-0 Unterberger, 1994, The Berezin transform and invariant differential operators, Comm. Math. Phys., 164, 563, 10.1007/BF02101491 Vershik, 1973, Representations of SL2(R), where R is function ring, Usp. Mat. Nauk, 28, 83 E. B. Vinberg, and, A. L. Onishchik, Linear Algebraic Groups. Wallach, 1979, Analytic continuation of discrete series, Trans. Amer. Math. Soc., 251, 19, 10.1090/S0002-9947-79-99965-3 G. Zhang, Berezin transform on line bundles over bounded symmetric domains, preprint, 1999.