Dunkl C.F., Xu Y. — Orthogonal Polynomials of Several Variables :: Электронная библиотека попечительского совета мехмата МГУ

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Dunkl C.F., Xu Y. — Orthogonal Polynomials of Several Variables

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Название: Orthogonal Polynomials of Several Variables

Авторы: Dunkl C.F., Xu Y.

Аннотация:

This is the first modern book on orthogonal polynomials of several variables, which are valuable tools used in multivariate analysis, including approximations and numerical integration. The book presents the theory in elegant form and with modern concepts and notation. It introduces the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains such as the cube, the simplex, the sphere and the ball. It also focuses on those of Gaussian type, for which fairly explicit formulae exist. The authors' approach blends classical analysis and symmetry-group-theoretic methods. The book will be welcomed by research mathematicians and applied scientists, including applied mathematicians, physicists, chemists and engineers.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 408

Добавлена в каталог: 02.02.2014

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

Предметный указатель

$\kappa$ -Bessel function      168
$\kappa$ -closed 1-form      162
$\kappa$ -exact      162
Abramowitz, M.      276 372
Adjoint map      170
Adjoint operator of $\mathcal{D}_{i}$ on $R^{d}$       184
Adjoint operator of $\mathcal{D}_{i}$ on $S^{d-1}$       182
Agahanov, C.A.      62 372
Akhiezer, N.I.      94 135 372
Alternating polynomial      140
Andrews, G.E.      xii 28 372
Aomoto, K.      254 372
Appell's polynomials      40
Appell, P.      x 28 37 40 46 49 61 133 136 254 372
Askey, R.      xii 28 203 266 284 371 372
Axler, S.      60 372
Badkov, V.      224 372
Bailey, W.N.      x 28 216 280 372
Baker, t.h.      254 335 350 372
Beerends, R.J.      254 325 335 373
Benson, C.T.      137 174 376
Berens, H.      61 62 135 281 284 373
Berg, C.      73 74 135 373
Bergeron, N.      325 373
Bertran, M.      135 373
Bessel function      219
beta function      1
Biorthogonal      33 111
Biorthogonal polynomials on $B^{d}$       43
Biorthogonal polynomials on $T^{d}$       49
Block Jacobi matrices      89
Block Jacobi matrices, truncated      114
Bojanov, B.      253 373
Bos, L.      284 373
Bourdon, B.      60 372
Braaksma, B.L.J.      60 373
Brinkman, H.C.      62 383
Buchstaber, V.      174 373
Calogero — Sutherland Systems      360
Calogero, F.      371 373
Cauchy kernel      214
Cesaro means      259
Chambers      142
Chambers, fundamental      142
Chebyshev polynomials      20
Chen, K.K.      285
Cheney, E.W.      284 373
Cherednik, I.      335 373
Chevalley, C.      173 373
Chihara, T.S.      29 373
Christensen, J.P.R.      73 373
Christoffel function      109
Christoffel — Darboux formula, one variable      10
Christoffel — Darboux formula, several variables      107
Chu — Vandermonde sum      4
Common zeros      113
Complete integrability      361
Completely monotone function      281
composition      288
Connett, W.C.      61 373
Constantine, A.G.      325 377
Cools, R.      136 381
Coxeter group      140 141
Coxeter, H.S.M.      137 142 173 174 374
Cubature formula      117 135
Cubature formula, Gaussian      119
Cubature formula, positive      118
de Feriet, J.K.      x 28 37 40 46 49 61 133 136 254 372
de Jeu, M.F.E.      158 375 377
Debiard, A      254 374
DeVore, R.A.      284 374
Didon, F.      40 62 133 136
Dieudonne, J.      xii 374
Dihedral group      144 205
Dijksma, A.      60 374
Disc polynomials      57
Dominance order      288
Dubiner, M.      61 374
Dunkl operator      137 152 240
Dunkl operator for abelian group $\mathbb{Z}^{d}_{2}$       197
Dunkl operator for dihedral groups      206
Dunkl, C.F.      60 62 158 174 223 224 253 335 336 370-372 374 375
Dunn, K.B.      254 375
Eier, R.      254 375
Engelis, G.K.      61 62 375
Engels, H.      136 375
Erdelyi, A.      x xi 28 37 40 46 49 61 63 112 133 136 213 248 253 254 285 375
Exton, H.      6 28 375
Fackerell, E.D.      61 375
Favard's theorem      79 93
Felder, G.      174 373
Finite reflection group      141
Finite reflection group, irreducible      142
Folland, G.B.      62 375
Forrester, P.J.      254 335 350 371 372
Fourier orthogonal series      105 110
Fourier transform      216
Freud, G.      29 73 284 375
Fuglede, B.      73 135 375
Funk — Hecke formula for h-harmonics      191
Funk — Hecke formula for ordinary harmonics      37
Funk — Hecke formula for polynomials on $B^{d}$       233
Gamma function      1
Garsia, A.M.      325 373
Gasper, G.      xii 279 281 284 375 376
Gaussian quadrature      12
Gaveau, B.      254 374
Gegenbauer polynomials      17
Gekhtman, M.I.      135 376
Generalized binomial coefficients      350
Generalized Fourier transform      216
Generalized Gegenbauer polynomials      26
Generalized Hermite polynomials      25
Generalized Pochhammer symbol      308
Goerlich, E.      276 376
Groemer, H.      60 376
Grove, L.C.      137 174 376
Grundmann, A.      48 61 376
h-harmonics      175
h-harmonics, projection operator      181
h-harmonics, space of      177
h-Laplacian      156
Hanlon, P.      336 375
harmonic oscillator      361
Harmonic polynomials      34
Haviland, E.K.      73 376
Heckman, G.J.      169 174 335 376
Helgason, S.      60 224 376
Hermite polynomials      14
Hermite polynomials, Cartesian      244
Hermite polynomials, spherical-polar      244
Hermite, C.      40 133 136
Higgins, J.R.      75 376
Hoffman, M.E.      254 376
Homogeneous polynomials      31
Hook length product      309
Hook length product, lower      321
Hook length product, upper      321
Horn, R.A.      70 80 376
Hua, L.K.      xii 376
Humphreys, J.E.      137 174
Hypergeometric function      3
Hypergeometric function, Gegenbauer polynomials      17 18
Hypergeometric function, Jacobi polynomials      21
Hyperoctahedral group      143
Hypersurface      119
Ignatenko, V.F.      151 376
Ikeda, M.      62 376
Inner product, biorthogonal type      311
Inner product, permissible      290

Inner product, torus      313
Intertwining operator      157
Invariant polynomials      148
Jack polynomials      304 325
Jack, H.      325 371 377
Jackson, D.      63 69 135 377
Jacobi polynomials      21
Jacobi polynomials on the disc      56 88
Jacobi polynomials on the square      56 85
Jacobi polynomials on the triangle      56 86
James, A.T.      325 377
Johnson, C.R.      70 80 376
Joint matrix      76
Kakei, S.      371 377
Kalnins, E.G.      223 377
Kalyuzhny, A.A.      135 376
Kanjin, Y.      62 377
Karlin, S.      62 377
Kato, Y.      371 377
Kim, Y.J.      61 377
Klimyk, A.U.      xii 62 381 382
Knop, K.      335 377
Koelink, E.      xii 377
Kogbetliantz, E.      266 377
Koornwinder, T.H.      x xii 55 60-62 254 374 377 381
Koschmieder, L.      285
Kowalski, M.A.      135 378
Krall, H.L.      60 63 135 378
Kwon, K.H.      61 377
Laguerre polynomials      15
Laplace operator      34
Laplace series      131 262
Lapointe, L.      335 371 378
Laporte, O.      174 378
Lassalle, M.      336 371 378
Lauricella functions      5
Leading coefficient      66
Lebedev, N.N.      x 320 378
Lee, J.K.      61 377
Legendre polynomials      20
length function      147
Li, Zh.-K.      285 286 378
Lidl, R.      254 375
Littlejohn, L.L.      61 378
Littler, R.A.      61 375
Logan, B.      253 378
Lorentz, G.G.      257 284 374 378
Lyskova, A.S.      61 378
MacDonald, I.G.      223 325 350 378
Maiorov, V.E.      253 378
Markett, C.      276 376 378
Mate, A.      284 378
McGregor, J.      62 377
Mehta, M.L.      378
Meulenbeld, B.      60 373
Miller, W.Jr.      223 377
Moeller, H.M.      48 61 135 376 379
moment      72
Moment functional      64
Moment functional, positive definite      67
Moment functional, quasi-definite      79
Moment problem      72
Moment problem, determinate      72
Moment sequences      72
Moment, Hamburger's theorem      73
Moment, matrix      64
Monomial      33
Monomial, orthogonal basis      33
Monomial, orthogonal polynomials      69
Monomial, orthogonal polynomials on ball      41
Monomial, orthogonal polynomials on simplex      47
Morrow, C.R.      136 379
Moser, W.O.J.      174
Mueller, C.      60 223 379
Multi-index notation      30
Multiple Hermite polynomials      49
Multiple Jacobi polynomials      37
Multiple Laguerre polynomials      51
Multiplicity function      152
Mysovskikh, I.P.      119 120 135 136 379
Nagy, B.Sz.      90 380
Nelson, E.      94 379
Nevai, P.      224 258 284 378 379
Nishino, A.      371 379
Nonsymmetric Jack polynomials      298 323
Nonsymmetric Jack — Hermite polynomials      334
Noumi, M.      xii 379
Nussbaum, A.E.      73 379
Okounkov, A.      335 379
Olshanski, G.      335 379
Opdam, E.M.      62 158 173 254 325 335 370 373 375 376 379
Order, dominance      288
Order, graded lexicographic      32
Order, lexicographic      32
Order, total      32
Orthogonal group      137
Orthonormal      33 68
Parabolic subgroup      146
Partition      288
Patterson, T.N.L.      136 379
Petrova, G.      253 373
Petrushev, P.      253 379
Pochhammer symbol      2
Podkorytov, A.M.      284 379
Poincare series      148
Poisson kernel      190
Positive roots      139
Proriol, J.      61 62 379
Putinar, M.      135 136 379
Radon, J.      135 379
Rahman, M.      xii 376
Ramey, W.      60 372
Ramirez, D.E.      60 375
Reproducing kernel      106
Reproducing kernel on the ball      131 232 233
Reproducing kernel on the simplex      242 243
Reproducing kernel on the sphere      131
Reproducing kernel, associated with $\mathbb{Z}^{d}_{2}$       202
Reproducing kernel, h-spherical harmonics      190
Ressel, P.      73 373
Reznick, B.      135 379
Ricci, P.E.      254 380
Riesz, F.      90 380
Roesler, M.      166 174 191 254 371 380
Root system      139
Root system, indecomposable      142
Root system, irreducible      142
Root system, rank of      141
Root system, reduced      139
Rosengren, H.      253 380
Rosier, M.      61 380
Roy, R.      xii 28 372
Rozenblyum, A.V.      380
Rozenblyum, L.V.      380
Rudin, W.      265 380
Saalschuetz formula      5
Sahi, S.      335 377 380
Schaake, G.      58 373
Schmid, H.      61 62 135 136 373
Schmuedgen, K.      73 380
Schwartz, A.L.      61 373 377
Selberg — Macdonald integral      347
Selberg, A.      350 380
Sheffer, I.M.      60 63 135 378
Shephard, G.C.      149 380
Shepp, I.      253 378
Shishkin, A.D.      62
Shohat, J.      73 135 380
Simple roots      142
Special orthogonal group      137

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