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Klimyk A.U., Vilenkin N.Ya. — Representation Theory and Noncommutative Harmonic Analysis II: Homogeneous Spaces, Representations and Special Functions
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 Functions

Авторы: 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: en

Рубрика: Математика/Симметрия и группы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 266

Добавлена в каталог: 30.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
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 $\mathcal{P}^{l}_{mn}(cos\theta)$      185
Addition theorem for functions $\mathfrak{P}^{l}_{mn}(cosh\ t)$      185
Addition theorem for functions $\mathfrak{P}^{\tau}_{mn}(cosh\ t)$      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 $\mathfrak{P}^{\tau}_{mn}(cosh\ t)$      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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