Wawrzynczyk A. — Group representations and special functions :: Электронная библиотека попечительского совета мехмата МГУ

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Wawrzynczyk A. — Group representations and special functions

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Название: Group representations and special functions

Автор: Wawrzynczyk A.

Аннотация:

This book in the MIA (East European) Series is precisely about special functions in their relation to analysis on homogeneous spaces, and is designed for students and researchers in one of the many fields where special functions are useful (such as, e.g., representation theory, mathematical physics, harmonic analysis).

Язык:

Рубрика: Математика/Симметрия и группы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1984

Количество страниц: 687

Добавлена в каталог: 05.05.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\Gamma$ -function      243—646
$\Gamma$ -function, duplication formula for      252
$\Gamma$ -function, Hankel integral representation for      255
$\Gamma$ -function, reflection formula for      247
$\xi$ -function      647
$\xi$ -function, number theoretic expression for      253
Abel transformation      370 384
Addition formulas      235
Ado theorem      50
Affine mapping      499
Algebra, abelian      89
Algebra, automorphism of      560
Algebra, central sequence of      89
Algebra, compact      561
Algebra, Lie, of a group      44
Algebra, nilpotent      89
Algebra, semi-simple      90
Algebra, simple      90
Algebra, solvable      90
Algebra, structure constants of      51
Algebra, universal enveloping      130
Ambrose's theorem      201
Atlas      15
Automorphism, inner      4
Automorphism, topological      8
b-function      253—646
Bargmann, V.      103
Bessel equation      268 278 650
Bessel functions      208 236 650
Bessel functions of first kind      457
Bessel functions of second kind      457
Bessel functions, addition formulas for      265 652
Bessel functions, Gegenbauer formula for      277
Bessel functions, generating function for      265 651
Bessel functions, multiplication formula for      277
Bessel functions, Poisson formula for      276 651
Bessel functions, recurrence formulas for      268
Bessel functions, Schlafli integral for      277 5
Bianchi's identities      486 491
Blattner, R.J.      116
Bochner — Weil theorem      167
Bochner, S.      142
Borel subgroup      586
Bruhat, F.      96 103 113 554 617
Bundle of forms      24 25
Bundle of k-vectors      25
Bundle of tensors of type (r,s)      24
Bundle, cotangent      24
Bundle, frame      21
Bundle, principal      62 478
Bundle, section of      25
Bundle, tangent      23
Bundle, trivial      22
Burnside theorem      204
Burnside, W.      173
Cartan centre of a group      13
Cartan decomposition of an algebra      573
Cartan numbers      597 598
Cartan of an algebra      29
Cartan subalgebra      569
Cartan theorem      540
Cartan, E.      91 241 475 532 536 540 558 570 584
Chart(s)      15
Chart(s), compatible      15
Chart(s), negatively oriented      69
Chart(s), positively oriented      69
Chevalley, C.      622
Christoffel symbols      497
Clebsch — Gordan coefficients      306 309
Commutation relations, canonical      138
Commutator      27
Confluent      465
Confluent hypergeometric function      649
Conjugacy class      6
Connection      484
Connection form      486
Connection, affine      488
Cosets, left      6
Cosets, right      6
Covering, two-fold      36
Curvature form      484
Curvature, sectional      507
Curve, lenght of      64
Curve, smooth      19
Derivations, inner, of algebra      29
Derivative, covariant      495
Diffeomorphism      17
Differential of a mapping      31
Distribution, k-dimensional      63
Dym, H.      214
Dynkin diagrams      570
Ehrenpreis, L.      643
Element, inverse      7
Element, neutral      7
Euler angles      236 287 288 349
Euler beta function      253 646
Euler function      240
Euler gamma function      243 646
Euler limit formula      254
Euler transformation      458
Expansions of functions corresponding to orthogonal polynomials      670
Expansions of functions on the sphere      669
Exponential mapping      495
Fell, I.M.G.      116
Fibre of a point      22
Fixed point property      587
Fourier transformation      667
Fourier transformation on a symmetric space      615
Fourier transformation on D      376
Fourier transformation on the circle group      667
Fourier transformation on the Lobatschevsky space $\mathscr{H}$       405
Fourier transformation, generalized      151
Fourier transformation, inversion formula for      376
Fourier transformation, Plancherel formula for      376
Fourier transformation, spherical on a symmetric space      618
Fourier transformation, spherical on the disc      369
Fourier — Bessel transformation      272
Frobenius theorem      183
Frobenius, G.      103 173
Function (s) $P^{l}_{fk}$       281 653
Function (s) $P^{l}_{fk}$ , addition formulas for      293—255
Function (s), associated $\chi$ -spherical      209
Function (s), central      195
Function (s), differentiable      16
Function (s), modular      75—76
Function(s) $P^{l}_{fk}$ , orthogonality relations for      291 292 654
Function(s) $P^{l}_{fk}$ , positively homogeneous      109
Function(s) $P^{l}_{fk}$ , spherical, mean value theorem for      267
Function(s) $P^{l}_{fk}$ , zonal $\chi$ -spherical      209
Fundamental form      515
Furstenberg, H.      359 412 488 613
Garding, L.      132
Gegenbauer equation      331
Gegenbauer equation polynomials      207 208 238 330 658
Gegenbauer equation, orthogonality relations for      335
Gelfand pair      221—222 225
Gelfand — Graev transformation      413
Gelfand — Graev transformation dual      415
Gelfand — Raikov construction      219 550
Gelfand — Raikov theorem      122
Gelfand, I.M.      96 103 122 152 207 242 370 413 545 559 643
Geodesic      494
Geodesic submanifold      590
Gindikin, S.G.      627 628
Godment, R.      141 207 476 613
Graev, M.I.      370 413 643
Graff's formula      265
Grassman algebra      24
Group      1
Group "ax + b"      4 41 258

Group of displacements      518
Group, abelian      1—92
Group, automorphism of      2
Group, character of      102
Group, commutative (abelian      1 92
Group, derived      93
Group, dual      165
Group, general linear      2
Group, Heisenberg — Weyl      51 137
Group, homomorphism of      2
Group, identity of      1
Group, infinitesimal generator of      3
Group, invariant, of a form      5
Group, isotropy      6
Group, Lie      41
Group, Lie, Lie algebra of      44
Group, Lie, one-parameter subgroup of      43
Group, local one-parameter      33
Group, locally compact      10
Group, motion      58—258
Group, motion proper      236—258
Group, nilpotent      92
Group, normalizer of      13
Group, orthogonal      5
Group, projective      66
Group, semi-simple      92
Group, simple      92
Group, solvable      92
Group, stability      6
Group, symplectic      5
Group, topological      9
Group, transformation      3
Group, transformation, homomorphism of      7
Group, transformation, isomorphism of      7
Group, transformation, topological      10
Group, transformation, transitive      6
Group, unimodular      76
Group, unitary      67
Haar measure      71
Haar, A.      71
Hansen formula      266
Harish — Chandra      152 207 476 477 559 621—627 631
Harish — Chandra c(•)-function      623
Harmonic functions on a symmetric space      613
Harmonic functions on the Lobatschevsky space $\mathscr{H}$       412
Harmonic functions, mean value formula for      208
Harmonic, spherical      233—315
Helgason, S.      384 544 559 594 625 629 631 634 642
Hermite polynomials      666
Hilbert — Schmidt (H—S) operators      175
Hilbert — Schmidt (H—S) operators, norm of      175
Hilbert — Schmidt (H—S) operators, spectral theorem for      177
Homogeneous topological space      10
Homomorphism, topological      8
Hopf mapping      68
Horocycle(s)      344—351 398 592
Horocycle(s), parallel      351
Horocycle(s), pencil of parallel      398
Horocyclic coordinates      368
Hurwitz measure      71—73
Hyperbolic space      389
Hypergeometric equation      452
Hypergeometric function      453—647
Hypergeometric function, confluent      465—649
Ideal(s)      28
Ideal(s), derived sequence of      90
Ideal(s), left-sided      200
Ideal(s), right-sided      200
Idempotent      200
Indical equation of the singularity      447
Inducing in "stages"      116
Intertwining number      144
Invariant, function      11
Involution      79
Isometry      504
Isomorphism, topological      8
Iwasawa decomposition      576 578
Iwasawa decomposition for SL(2,C)      390
Iwasawa decomposition for SL(2,R)      347
Jacobi equation      469
Jacobi functions      238—239 357 660
Jacobi functions, mean value formula for      362
Jacobi identity      28
Jacobi polynomials      207—236 237 279 281 653
Jacobian matrix      18
Johnson, D.L.      384
K-multipler      211
Karpelewic, F.I.      627 628
Killing form      90
Kostant, B.      617
Laguerre equation      469
Laguerre equation, associated      469
Laguerre polynomials      664
Laplace — Beltrami operator      289—302 411
Legendre equation      658
Legendre equation, associated      360
Legendre functions      208—238 239 257 663
Legendre functions, addition formula for      384
Legendre functions, associated      236—237 239 281 317 656 662
Legendre polynomials      208—236 237 240 279 281 341 657 664
Legendre polynomials, generating function for      316—664
Legendre polynomials, integral formula for      315—664
Legendre polynomials, orthogonality relations for      441—665
Legendre polynomials, spherical equation for      293
Level set      35
Lie (Palais) theorem      56
Lie algebra      28—44
Lie bracket      27
Lie, S.      56
Lobatchevsky space      394 589
Loos, O.      521 537
Lorentz group, proper      395
Mackey, G.      86 96 103 136
Manifold, analytic      16
Manifold, differentiable      16
Manifold, orientation of      62
Manifold, parallelizable      38
Manifold, Riemannian      63
Mapping, analytic      16
Mapping, compact      199
Mapping, differentiable (smooth      16
Mapping, exponential      45
Matrix element      125
Matrix orthogonality relations for      190
Matrix, Jacobian      18
Matrix, upper triangular      5
Maurer — Cartan equation      482
Maurin, K.      551 553
Mautner, F.      140 141 151 643
Mc Kean      214
Measure(s), convolution of      77
Measure(s), invariant      85
Measure(s), positive definite (P.D.)      118
Measure(s), quasi-invariant      85
Mehler — Fok transformation      373—670
Mellin transformation      159 246 667
Minkovsky space      411
Multiplier(s)      107 211
Multiplier(s), cohomological      135
Murphy formula      383
Naimark, M.A.      103 146 151
Nomizu, K.      483
Occurence number      144
Operator, compact      199
Operator, d'Alembert      411
Operator, decomposable      149
Operator, diagonal      149
Operator, intertwining      115
Operator, Laplace      156
Operator, Laplace — Beltrami      289 302 411

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