|
|
|
|
References
|
|
| |
| 1. |
G. S. Andrews, R. Askey, R. Roy, Special Functions, Cambridge Univ. Press, 1999 |
| 2. |
M. F. Atiyah, “Resolution of singularities and division of distributions”, Comm. Pure Appl. Math., 23 (1970), 145–150 |
| 3. |
E. P. van den Ban, H. Schlichtkrull, “Fourier inversion on a reductive symmetric space”, Acta Math., 182:1 (1999), 25–85 |
| 4. |
E. P. van den Ban, H. Schlichtkrull, “The most continuous part of the Plancherel decomposition for
a reductive symmetric space”, Ann. Math. (2), 145:2 (1997), 267–364 |
| 5. |
V. Bargmann, “Irreducible unitary representations of the Lorentz group”, Ann. Math., 48 (1947), 568–640 |
| 6. |
F. A. Berezin, “Quantization in complex symmetric spaces”, Izv. Akad. Nauk SSSR, Ser. Math., 39:2 (1975), 363–402 |
| 7. |
F. A. Berezin, “On relations between covariant and contravariant symbols of operators
for complex classical domains”, Dokl. Akad Nauk SSSR, 241:1 (1978), 15–17 |
| 8. |
M. Berger, “Les espaces symétriques noncompacts”, Ann. Sci. École Norm. Sup., 74 (1957), 85–177 |
| 9. |
I. M. Bernshtein, “Analytic continuation of generalized functions with respect to
a parameter”, Funkts. Anal. Prilozhen., 6:4 (1972), 26–40 |
| 10. |
W. Bertram, The Geometry of Jordan and Lie Structures, Lect. Notes Math., 1754, Springer-Verlag, Berlin, 2000 |
| 11. |
T. Branson, G. Olafsson, B. Ørsted, “Spectrum generating operators and intertwining operators for
representations induced from a maximal parabolic subgroup”, J. Funct. Anal., 135:1 (1996), 163–205 |
| 12. |
P. Delorme, “Formule de Plancherel pour les espaces symétriques réductifs”, Ann. Math. (2), 147:2 (1998), 417–452 |
| 13. |
G. van Dijk, S. C. Hille, “Canonical representations related to hyperbolic spaces”, J. Funct. Anal., 147 (1997), 109–139 |
| 14. |
G. van Dijk, V. F. Molchanov, “The Berezin form for rank one para-Hermitian symmetric spaces”, J. Math. Pure. Appl., 78 (1999), 99–119 |
| 15. |
G. Dijk, M. Pevzner, “Berezin kernels of tube domains”, J. Funct. Anal., 181:2 (2001), 189–208 |
| 16. |
A. Dvorsky, S. Sahi, “Explicit Hilbert spaces for certain unipotent representations, II”, Invent. Math., 138:1 (1999), 203–224 |
| 17. |
A. Dvorsky, S. Sahi, “Explicit Hilbert spaces for certain unipotent representations, III”, J. Funct. Anal., 201:2 (2003), 430–456 |
| 18. |
J. Faraut, A. Koranyi, Analysis on Symmetric Cones, The Clarendon Press, Oxford, 1994 |
| 19. |
M. Flensted-Jensen, “Discrete series for semisimple symmetric spaces”, Ann. Math. (2), 111:2 (1980), 253–311 |
| 20. |
I. M. Gelfand, M. I. Graev, A. M. Vershik, “Models of representations of current groups”, Representations of Lie Ggroups and Lie Algebras (Budapest, 1971), Akad. Kiado, Budapest, 1985, 121–179 |
| 21. |
I. M. Gelfand, M. A. Naimark, “Unitary representations of the Lorentz group”, Izv. Akad. Nauk SSSR., Ser. Mat., 11 (1947), 411–504 |
| 22. |
I. M. Gelfand, M. A. Naimark, Unitary Representations of the Classical Groups, Trudy Mat. Inst. Steklov., 36, Izdat. Akad. Nauk SSSR, Moscow–Leningrad, 1950 |
| 23. |
S. G. Gindikin, F. I. Karpelevich, “On an integral connected with symmetric Riemannian space of nonpositive curvature”, Izv. Akad. Nauk SSSR, Ser. Mat., 30 (1966), 1147–1156 |
| 24. |
W. Groenevelt, Tensor product representations and special functions, Ph. D. Thesis, Deift University, 2004 |
| 25. |
P. Harinck, “Plancherel formula pour $\mathrm{GL}(n,\mathbb{C})/\mathrm{U}(p,q)$”, J. Reine Angew. Math., 428 (1992), 45–95 |
| 26. |
P. Harinck, “Fonctions orbitales sur $G_\mathbb{C}/G_\mathbb{R}$. Formule
d'inversion des intégrales orbitales et formule de Plancherel”, J. Funct. Anal., 153 (1998), 52–107 |
| 27. |
Harish-Chandra, “Harmonic analysis on real semisimple groups. III: The Maas–Selberg
relations and the Plancherel formula”, Ann. Math., 104 (1976), 117–201 |
| 28. |
G. Heckman, H. Schlichtkrull, Harmonic Analysis and Special Functions on Symmetric Spaces, Academic Press, San Diego, 1994 |
| 29. |
S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York–London, 1962 |
| 30. |
S. Helgason, Groups and Geometric Analysis. Integral Geometry, Invariant Differential
Operators, and Spherical Functions, Academic Press, Orlando, 1984 |
| 31. |
S. C. Hille, Canonical representations, Ph. D. Thesis, Leiden University, 1999 |
| 32. |
Hua Loo-Keng, Harmonic Analysis of Functions of Several Complex Variables in Classical Domains, Beijing, 1958 |
| 33. |
H. P. Jakobsen, M. Vergne, “Restrictions and expansions of holomorphic representations”, J. Funct. Anal., 34:1 (1979), 29–53 |
| 34. |
K. W. J. Kadell, “The Selberg–Jack symmetric functions”, Adv. Math., 130:1 (1997), 33–102 |
| 35. |
A. A. Kirillov, Elements of Representation Theory, Nauka, Moscow, 1972 |
| 36. |
A. W. Knapp, E. M. Stein, “Intertwining operators for semisimple groups”, Ann. Math. (2), 93 (1971), 489–578 |
| 37. |
I. G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd edition. With contributions by A. Zelevinsky, Oxford Univ. Press, New York, 1995 |
| 38. |
B. O. Makarevich, “Open symmetric orbits of reductive groups in symmetric $R$-spaces”, Mat. Sb., 91(133) (1973), 390–401, 472 |
| 39. |
V. F. Molchanov, “Decomposition of the tensor square of a representation of the
complementary series of a group”, Funkts. Anal. Prilozhen, 9:4 (1975), 79–80 |
| 40. |
V. F. Molchanov, “Tensor products of unitary representations of the three-dimensional
Lorentz group”, Izv. Akad. Nauk SSSR, Ser. Mat., 43:4 (1979), 860–891 |
| 41. |
V. F. Molchanov, “Plancherel's formula for the pseudo-Riemannian space SL $(3,R)/$GL $(2,R)$”, Sib. Mat. Zh., 23:5 (1982), 142–151, 224 |
| 42. |
V. F. Molchanov, “The Plancherel formula for pseudo-Riemannian symmetric spaces of rank 1”, Dokl. Akad. Nauk SSSR, 290:3 (1986), 545–549 |
| 43. |
V. G. Molchanov, “Harmonic analysis on homogeneous spaces”, Representation Theory and Noncommutative Harmonic Analysis, II, Encyclopaedia Math. Sci., 59, Springer, Berlin, 1995, 1–135 |
| 44. |
N. Mukunda, “Unitary representations of the Lorentz groups: Reduction of the
supplementary series under a noncompact subgroup”, J. Math. Phys., 9 (1968), 417–431 |
| 45. |
M. Muro, “Singular invariant hyperfunctions on the space of complex and
quaternion Hermitian matrices”, J. Math. Soc. Japan, 53:3 (2001), 589–602 |
| 46. |
T. Nagano, “Transformation groups on compact symmetric spaces”, Trans. Amer. Math. Soc., 118 (1965), 428–453 |
| 47. |
M. A. Naimark, “Decomposition of a tensor product of irreducible representations of the proper Lorentz group into irreducible representations. I: The case of a tensor product of representations of the fundamental series”, Trudy Moskov. Mat. Obšč, 8, 1959, 121–153 |
| 48. |
M. A. Naimark, “Decomposition of a tensor product of irreducible representations of the proper Lorentz group into irreducible representations. II: The case of a tensor product of representations of the fundamental and complementary series”, Trudy Moskov. Mat. Obšč, 9, 1960, 237–282 |
| 49. |
M. A. Naimark, “Decomposition of a tensor product of irreducible representations of the proper Lorentz group into irreducible representations, III”, Trudy Moskov. Mat. Obšč, 10, 1961, 181–216 |
| 50. |
Yu. A. Neretin, “Discrete occurrences of representations of the complementary series in tensor products of unitary representations”, Funkts. Anal. Prilozhen, 20:1 (1986), 79–80 |
| 51. |
Yu. A. Neretin, “Conformal geometry of symmetric spaces, and generalized linear fractional Krein–Smul'yan mappings”, Mat. Sb., 190:2 (1999), 93–122 |
| 52. |
Yu. A. Neretin, Categories of Symmetries and Infinite-Dimensional Groups, Oxford Univ. Press, New York, 1996 |
| 53. |
Yu. A. Neretin, “Pseudoriemannian symmetric spaces: one type realizations and open embeddings to Grassmannians”, Zap. Nauchn. Semin. POMI, 256, 1999, 145–167 ; arXiv: /math/9905014 |
| 54. |
Yu. A. Neretin, “Matrix analogs of $B$-function and Plancherel formula for Berezin kernel representations”, Mat. Sb., 191:5 (2000), 67–100 ; arXiv: /math.RT/9905045 |
| 55. |
Yu. A. Neretin, “On the separation of spectra in the analysis of Berezin kernels”, Funkts. Anal. Prilozhen., 34:3 (2000), 49–62 |
| 56. |
Yu. A. Neretin, “Plancherel formula for Berezin deformation of $L^2$ on Riemannian
symmetric space”, J. Funct. Anal., 189 (2002), 336–408 ; arXiv: /math.RT/9911020 |
| 57. |
Yu. A. Neretin, “Matrix balls, radial analysis of Berezin kernels, and hypergeometric determinants”, Moscow Math. J., 1:2 (2001), 157–220 |
| 58. |
Yu. A. Neretin, “The index hypergeometric transform and an imitation of the analysis
of Berezin kernels on hyperbolic spaces”, Mat. Sb., 192:3 (2001), 83–114 |
| 59. |
Yu. A. Neretin, “he action of an overalgebra in the Plancherel decomposition and shift
operators in an imaginary direction”, Izv. Ross. Akad. Nauk Ser. Mat., 66:5 (2002), 171–182 |
| 60. |
Yu. A. Neretin, “The beta function of the Bruhat–Tits building and the deformation of the space $l\sp 2$ on the set of $p$-adic lattices”, Mat. Sb., 194:12 (2003), 31–62 |
| 61. |
Yu. A. Neretin, Some continuous analogs of expansion in Jacobi polynomials and vector valued hypergeometric orthogonal bases, arXiv: /math.CA/0309445 |
| 62. |
Yu. A. Neretin, Notes on Sobolev spaces on compact classical groups and Stein–Sahi representations, arXiv: /math.RT/0411420 |
| 63. |
Yu. A. Neretin, A class of kernels on pseudo-Riemannian symmetric spaces, in preparation |
| 64. |
Yu. A. Neretin, G. I. Olshanskii, “Boundary values of holomorphic functions, singular unitary representations of groups $O(p,q)$ and their limits as $q\to\infty$”, Zap. Nauchn. Semin. POMI, 223, 1995, 9–91 ; http://wwwth.itep.ru/~neretin |
| 65. |
G. I Olshansky, “Irreducible unitary representations of the groups $\mathrm U(p,q)$ that allow passage to a limit as $q\to\infty$”, Zap. Nauchn. Semin. LOMI, 172, 1989, 114–120 |
| 66. |
T. Oshima, “A method of harmonic analysis on semisimple symmetric spaces”, Algebraic Analysis, II, Academic Press, Boston, 1988, 667–680 |
| 67. |
T. Oshima, “A calculation of $c$-functions for semisimple symmetric spaces”, Lie Groups and Symmetric Spaces, Amer. Math. Soc. Transl., Ser. 2, 210, Amer. Math. Soc., Providence, RI, 2003, 307–330 |
| 68. |
T. Oshima, T. Matsuki, “A description of discrete series for semisimple symmetric spaces”, Adv. Stud. Pure Math., 4 (1984), 331–390 |
| 69. |
T. Oshima, J. Sekiguchi, “Eigenspaces of invariant differential operators on a semisimple
symmetric space”, Inv. Math., 57 (1980), 1–81 |
| 70. |
A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev, Integrals and Series. More Special Functions, V. 3, Gordon and Breach Science Publishers, New York, 1990 |
| 71. |
I. I. Pyateskii-Shapiro, Automorphic Functions and the Geometry of Classical Domains, Fizmatlit, Moscow, 1961 |
| 72. |
L. Pukanszky, “On the Kronecker products of irreducible unitary representations of the $2\times2$ real unimodular group”, Trans. Amer. Math. Soc., 100 (1961), 116–152 |
| 73. |
M. Rais, Distributions Homogènes sur des Espaces de Matrices, Bull. Soc. Math. France Mém., 30, 1972, Supplément |
| 74. |
F. Ricci, E. M. Stein, “Homogeneous distributions on spaces of Hermitian matrices”, J. Reine Angew. Math., 368 (1986), 142–164 |
| 75. |
S. Sahi, “A simple construction of Stein's complementary series representations”, Proc. Amer. Math. Soc., 108:1 (1990), 257–266 |
| 76. |
S. Sahi, “Unitary representations on the Shilov boundary of a symmetric tube domain”, Representation theory of groups and algebras, Contemp. Math., 145, American Mathematical Society, Providence, RI, 1993, 275–286 |
| 77. |
S. Sahi, “Jordan algebras and degenerate principal series”, J. Reine Angew. Math., 462 (1995), 1–18 |
| 78. |
S. Sahi, “Explicit Hilbert spaces for certain unipotent representations”, Inv. Math., 110:2 (1992), 409–418 |
| 79. |
S. Sahi, E. M. Stein, “Analysis in matrix space and Speh's representations”, Inv. Math., 101:2 (1990), 379–393 |
| 80. |
M. Sato, T. Shintani, “On zeta functions associated with prehomogeneous vector spaces”, Ann. Math. (2), 100 (1974), 131–170 |
| 81. |
E. M. Stein, “Analysis in matrix spaces and some new representations of $\mathrm{SL}\,(N,C)$”, Ann. Math. (2), 86 (1967), 461–490 |
| 82. |
A. Unterberger, H. Upmeier, “The Berezin transform and invariant differential operators”, Comm. Math. Phys., 164 (1994), 563–597 |
| 83. |
M. Vergne, H. Rossi, “Analytic continuation of the holomorphic discrete series of a semi-simple Lie group”, Acta Math., 136:1–2 (1976), 1–59 |
| 84. |
A. M. Vershik, I. M. Gelfand, M. I. Graev, “Representations of the group $\mathrm{SL}\,(2,R)$, where $R$ is a ring of functions”, Uspekhi Mat. Nauk, 28:5(173) (1973), 83–128 |
| 85. |
N. Yu. Vilenkin, Special Functions and Theory of Group Representations, Nauka, Moscow, 1965 |
| 86. |
N. Ya. Vilenkin, A. U. Klimyk, Representations of Lie Groups and Special Functions, Vol. 1–2, Kluwer, 1991 |
| 87. |
D. A. Vogan, “The unitary dual of $\mathrm{GL}(n)$ over an Archimedean field”, Inv. Math., 83:3 (1986), 449–505 |
| 88. |
G. Zhang, “Berezin transform on line bundles over bounded symmetric domains”, J. Lie Theory, 10:1 (2000), 111–126 |
| 89. |
G. Zhang, “Branching coefficients of holomorphic representations and Segal–Bargmann transform”, J. Funct. Anal., 195:2 (2002), 306–349 |