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Klimyk A.U., Vilenkin N.Ya. — Representation Theory and Noncommutative Harmonic Analysis II: Homogeneous Spaces, Representations and Special Functions
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Название: Representation Theory and Noncommutative Harmonic Analysis II: Homogeneous Spaces, Representations and Special FunctionsАвторы: Klimyk A.U., Vilenkin N.Ya. Аннотация: This volume of the Encyclopaedia contains two contributions: the first one, "Harmonic Analysis on Homogeneous Spaces", is written by V.F.Molchanov, the second one, "Representations of Lie Groups and Special Functions", by N.Ya. Vilenkin and A.U. Klimyk. Molchanov focuses on harmonic analysis on semi-simple spaces, whereas Vilenkin and Klimyk treat group theoretical methods also with respect to special functions, orthogonal polynomials and integral transforms. Both contributions are surveys introducing readers to the above topics and preparing them for the study of more specialised literature. This book will be very useful to students and researchers in mathematics, theoretical physics and those chemists dealing with quantum systems.
Язык: Рубрика: Математика /Симметрия и группы /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1995Количество страниц: 266Добавлена в каталог: 30.04.2005Операции: Положить на полку |
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Abel, N.H. 142 Action, almost effective 16 Action, effective 16 Action, transitive 16 Addition theorem for Bessel functions 186 187 Addition theorem for Charlier polynomials 248 Addition theorem for functions 185 Addition theorem for functions 185 Addition theorem for functions 185 Addition theorem for Gegenbauer polynomials 186 Addition theorem for Hermite polynomials 190 Addition theorem for Jacobi functions 188 Addition theorem for Jacobi polynomials 187 Addition theorem for Krawtchouk polynomials 245 Addition theorem for Laguerre polynomials 189 Addition theorem for Legendre functions 185 Addition theorem for spherical functions 184 Alain, P.N.D. 249 Algebra Lie, compact 13 Algebra Lie, exponential 13 Algebra Lie, reductive 13 Algebra Lie, semisimple 13 Algebra Lie, simple 13 Algebra Lie, symmetric 18 Algebra Lie, symmetric, dual 27 Algebra Lie, symmetric, effective 18 Algebra Lie, symmetric, irreducible 20 Algebra Lie, symmetric, pseudo-Riemannian 21 Alishauskas, S.I. 249 Andrews, G.E. 249 Anslander, L. 145 249 Ardalan, F. 7 128 Askey, R. 149 242 246 249 Baily, W.N. 249 Bannai, E. 152 249 Bargmann, V. 145 249 Basis, canonical 164 Basis, elliptic 208 Basis, hyperbolic 208 Basis, parabolic 208 Basu, D. 208 212 249 Bateman, H. 143 Benoist, y. 45 127 Berezin, F.A. 4 6 127 128 151 250 251 Berger, M. 4 20 21 128 Bernoulli, D. 142 Bernstein, I.N. 95 128 Biedenharn, L.C. 151 242 246 250 254 Bien, F. 58 128 Binomial distribution 236 Blind, B. 6 7 128 Bochner, S. 151 Bopp, N. 6 128 Borel, A. 6 128 Bourbaki, N. 12 128 Boyer, C.P. 7 128 Braaksma, B. 250 Bruhat, F. 60 128 Cahen, M. 21 128 144 145 Cartan, E. 4 63 128 centralizer 10 CHARACTER 175 Chebyshev, P.L. 143 148 Clerc, J.L. 250 Coefficient, Clebsch — Gordan 149 224 241 Coefficient, Racah 175 Commutant 44 Complexification of a symmetric space 23 Component of a group, split 16 Component, Fourier 8 34 102 Constantine, A.G. 151 253 Convolution 8 35 Decomposition, canonical 19 Decomposition, Cartan 27 156 Decomposition, Cartan — Berger 24 Decomposition, Gauss 25 156 Decomposition, Iwasawa 16 156 Decomposition, Langlands 16 Degree (dimension) formal 40 Delorme, P. 6 61 129 Diagonal 4 20 distribution 11 12 Distribution, extremal 36 Distribution, positive-definite 35 Doebner, H.D. 252 Duality principle 56 57 Dunford, N. 113 114 117 129 Dunkl, C.F. 152 250 Durand, L. 250 Eigenspace joint 4 Element, Casimir 14 Element, invariant 200 Element, q-regular 23 Element, semisimple 13 Equivariant 8 34 Erdelyi, A. 103 104 105 106 129 143 250 Euler angles 201 Euler, L. 142 Factor space 16 Faraut, J. 5 7 39 52 97 98 119 129 Fedenko, A.S. 20 129 Feinsilver, P.J. 152 250 252 Flensted-Jensen, M. 6 26 41 56 59 61 129 234 250 Formula, Burchnall — Chaundy 226 Formula, inversion 10 43 Formula, Plancherel 10 36 43 231 232 Formula, Plancherel, partial 40 Function of a cone 232 Function, associated spherical 142 174 Function, basic hypergeometric 152 Function, belonging to a representation 171 Function, c-function 50 Function, central 176 Function, density 31 Function, generating 196 Function, Harish-Chandra 233 Function, harmonic 43 Function, Heaviside 11 Function, hypergeometric 142 Function, hypergeometric, generalized 144 Function, K-finite 57 Function, Krawtchouk — Meixner 240 Function, positive-definite 9 Function, spherical 4 8 34 142 Function, Wigner 149 Function, zonal spherical 142 174 Gallard, P.-Y. 6 7 129 Gangolli, R. 6 129 Gasper, G. 246 249 250 Gauss, C.F. 142 143 Gavrilik, A.M. 151 183 254 Gel'fand, I.M. 4 5 6 7 12 41 82 100 127 129 130 135 145 149 151 183 251 252 257 Gel'fand, S.I. 95 128 251 Gelbart, S. 250 Gindikin, S.G. 5 41 47 130 151 252 Godement, R. 252 Gorbatsevich, V.V. 18 130 Graev, M.I. 5 6 7 129 135 151 183 251 Greiner, P.C. 252 Gross, K.I. 252 Group Lie, exponential 13 Group Lie, reductive 13 Group Lie, semisimple 4 Group, adjoint 13 Group, Heisenberg 160 Group, Poincare 160 Gruber, B. 7 96 97 131 252 Gunson, J. 249 Gustafson, R.A. 252 Harinck, P. 6 128 Harish-Chandra 5 7 12 26 39 41 52 108 130 145 171 252 Harish-Chandra c-function 233 Harzallah, K. 7 39 129 Helgason, S. 4 6 7 12 18 20 21 26 28 32 39 45 52 53 56 63 131 233 252 Herz, C.S. 151 253 Hilgert, J. 41 130 Holman, W.J. 252 253 Hoogenboom, B. 253 Hyperfunction 11 12 Ikeda, M. 253 Involution 13 Involution, Cartan 14 Ismagilov, R.S. 6 131 Isomorphism of symmetric spaces 18 Isomorphism, Harish-Chandra 30 Ito, T. 152 249 James, A.T. 151 253 Janson, S. 253 Johnson, K.D. 52 131 Juice, J. 145 Kac, V.G. 253 Kalnins, E.G. 208 253 Kapranov, M.M. 251 Karabegov, A.V. 6 131 Karlin, S. 253 Karpelevich, F.I. 5 47 60 129 131 151 250 Kashiwara, M. 6 52 131 Kaufman, B. 253 Kengmana, T. 6 108 131 Kernel of an action 16 Khersonskij, V.K. 242 246 257 Khudyakova, G.I. 183 257 Kil'dyushev, M.S. 147 253 Kirillov, A.A. 7 8 12 37 39 45 62 72 131 145 163 253 Klein, F. 142 Klesova, L.M. 151 257 Klimyk, A.U. 7 96 97 131 149 151 153 154 183 208 217 211 236 245 247 253 254 258 Klink, W.H. 254 Knapp, A.W. 52 131 Kobayashi, S. 14 18 21 26 28 78 131 Koh, S.S. 4 20 131 Koornwinder, T.H. 7 131 149 188 234 236 243 249 254 Koranyi, A. 52 130 254 Kosters, M.T. 6 7 131 Kosters, W.A. 5 7 83 86 119 131 Kowata, A. 131 Kuchment, P.A. 52 132 Kunze, R.A. 252 Laplace, P.S. 142 144 Lebedev, N.N. 254 Legendre, A.M. 142 144 Lepowsky, J. 254 Levinson, I.B. 242 259 Lewis, J.B. 49 52 132 Lichnerowicz, A. 29 32 132 Limic, N. 5 7 132 Lindblad, G. 259 Loos, O. 21 26 28 132 Louck, J.D. 151 242 246 250 254 Maass, H. 151 254 MacDonald, I.G. 254 MacGregor, J.L. 253 Magnus, W. 129 250 Manifold pseudo-Riemannian 12 Matsuki, T. 6 26 41 58 75 132 134 Matsumoto, S. 5 7 132 McBride, E.B. 254 Metric pseudo-Riemannian 12 Meulenbeld, B. 250 Mickelson, J. 183 255 Miller, W. 168 247 255 Milne, S.C. 252 255 Minemura, K. 131 Minlos, R.A. 251 Molchanov, V.F. 5 6 7 8 41 96 97 98 108 119 120 132 133 Moody, R.V. 255 Moore, C.C. 145 249 Moskalev, A.I. 242 246 257 Mukunda, N. 7 133 Multiplicity 156 Naimark, M.A. 145 251 Niederle, J. 5 7 131 133 183 255 Nikiforov, A.F. 147 255 Nizhnikov, A.I. 258 Nomizu, K. 14 18 21 26 28 78 131 normalizer 10 Oberhettinger, F. 129 250 Okamoto, K. 6 41 129 131 Olafeson, G. 41 131 133 Olevskij, M.N. 255 Onishchik, A.L. 12 18 130 135 Operator, adjoint 11 Operator, differential 11 Operator, differential, invariant 28 Operator, intertwining 92 Operator, Laplace 200 202 Operator, Laplace — Beltrami 12 200 Operator, symmetric 31 Orbit 16 Orbit, regular (singular) 78 Orsted, B. 41 131 133 Oshima, T. 6 26 29 32 41 49 52 58 60 61 75 131 133 134 Pair, Gelfand 42 Pair, generalized Gelfand 44 Paranuk, V.I. 151 255 258 Parker, M. 21 128 Parseval equality 170 Part, radial 31 Part, vector 14 Patera, J. 255 Pavlyuk, A.P. 151 257 Peetre, J. 253 Peter, F. 146 Plancherel measure 171 Poel, M. 5 7 32 96 129 134 Polynomials, Charlier 240 Polynomials, Hahn 243 Polynomials, Hahn, dual 244 Polynomials, Hahn, of imaginary argument 225 Polynomials, Krawtchouk 236 Polynomials, Meixner 237 238 Polynomials, Pollaczek — Meixner 212 Polynomials, Racah 247 Product formula for Bessel functions 194 Product formula for Charlier polynomials 248 Product formula for functions 193 Product formula for Gegenbauer polynomials 194 Product formula for Jacobi functions 195 Product formula for Jacobi polynomials 193 195 Product formula for Krawtchouk polynomials 245 Product formula for Laguerre polynomials 195 Product formula for Legendre functions 194 Product formula for Legendre polynomials 194 Product formula for Meixner polynomials 246 Product formula for spherical functions 43 193 Product of symmetric spaces, direct 18 Product, inner, non-local 6 Raczka, R. 5 7 132 Radical unipotent 16 Rank of a Lie algebra 14 Rank of a Lie group 14 Rank of a symmetric Lie algebra 23 Rank of a symmetric space 23 Rank, split 23 Real rank 15 155 Representation, adjoint 13 Representation, continuous series 46 92 Representation, discrete series 39 Representation, irreducible 146 Representation, quasi-regular 3
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