Vilenkin N.Ja., Klimyk A.U. — Representation of Lie Groups and Special Functions: Volume 1: Simplest Lie Groups, Special Functions and Integral Transforms :: Электронная библиотека попечительского совета мехмата МГУ

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Vilenkin N.Ja., Klimyk A.U. — Representation of Lie Groups and Special Functions: Volume 1: Simplest Lie Groups, Special Functions and Integral Transforms

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Название: Representation of Lie Groups and Special Functions: Volume 1: Simplest Lie Groups, Special Functions and Integral Transforms

Авторы: Vilenkin N.Ja., Klimyk A.U.

Аннотация:

This is the first of three major volumes which present a comprehensive treatment of the theory of the main classes of special functions from the point of view of the theory of group representations. This volume deals with the properties of classical orthogonal polynomials and special functions which are related to representations of groups of matrices of second order and of groups of triangular matrices of third order. This material forms the basis of many results concerning classical special functions such as Bessel, MacDonald, Hankel, Whittaker, hypergeometric, and confluent hypergeometric functions, and different classes of orthogonal polynomials, including those having a discrete variable. Many new results are given. The volume is self-contained, since an introductory section presents basic required material from algebra, topology, functional analysis and group theory. For research mathematicians, physicists and engineers.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 640

Добавлена в каталог: 09.02.2014

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Предметный указатель

Algebra      7
Algebra, Banach      34
Algebra, Heisenberg      50
Algebra, Lie      8
Algebra, Lie, commutative      9
Algebra, Lie, compact      48
Algebra, Lie, nilpotent      49
Algebra, Lie, reductive      48
Algebra, Lie, semisimple      48
Algebra, Lie, simple      48
Algebra, Lie, solvable      49
Algebra, quotient      14
Automorphism      11
Automorphism of a group      11
Automorphism of a group, inner      13
Automorphism of an algebra      14
Automorphism, involutive      55
Basis      7
Basis, biorthogonal      18
Basis, canonical      278
Basis, orthonormal      26
Beta-function      136
Center      11
Center of a group      10
Center of a Lie algebra      11
centralizer      10
Centralizer of a group      10
Centralizer of a ring      11
Character of a representation      88
Closure of a set      19
Coefficient, Clebsch — Gordan      499
Coefficient, Clebsch — Gordan, of S      562
Coefficient, Clebsch — Gordan, of SU(1, 1)      571
Coefficient, Clebsch — Gordan, of SU(2)      499
Coefficient, Racah      528
Commutator      7
Commutator subalgebra      11
Commutator subgroup      10
Complexification      42
Complexification of Lie algebras      42
Complexification of Lie groups      42
Composition of mappings      6
Cone      77
Coset      9
Coset, two-sided      9
Cosine, hyperbolic      110
Curve, integral      20
Decomposition      56
Decomposition of a group      58
Decomposition of regular representation      100
Decomposition, Cartan      57
Diffeomorphism      21
Differential of a mapping      21
Differentiation of an algebra      15
Dimension of a representation      67
Duality by Cartan      58
Eigenvalue      30
Eigenvector      30
Elements of a group, conjugate      13
Equality, Liapunov — Steklov      26
Equation, Bessel      148 194
Equation, Bessel, modified      151
Equation, characteristic      31
Equation, hypergeometric      389
Equation, hypergeometric, confluent      224
Equation, Whittaker      216
Euler angles      268
Euler angles, complex      270
Expansion in spherical functions      104
Expansion of function on a group      99
Field      7
Field, tangent vector      20
Flag      53
Flag, signature of      53
FORM      16
Form, bilinear      16
Form, bilinear, non-degenerate      16
Form, bilinear, skew-symmetric      17
Form, cubic      16
Form, Hermitian      17
Form, Killing      46
Form, of degree n      16
Form, quadratic      16
Form, real      42
Form, real of a Lie algebra      42
Form, real of a Lie group      42
Form, sesquilinear      16
Form, strictly positive      17
Formula, Abel      157
Formula, Burchnall — Chaundy      527
Formula, Christoffel — Darboux      252 339 343
Formula, convolution      118
Formula, Dougall      147
Formula, Rodrigues for $C^\alpha_n$       291
Formula, Rodrigues for $P_n^{\alpha,\beta}$       289
Formula, Rodrigues for $P_{mn}^\ell$       286
Formula, Rodrigues for       357
Formula, Rodrigues for       357
Formula, Whipple      542
Fourier series      99 113
Fourier series, coefficient of      99
Function, $P_{mn}^\ell$       284
Function, $\mathfrak{P}_{mn}^\tau$       312
Function, $\mathfrak{P}_{\lambda\mu}^\tau$       397
Function, $\mathfrak{Q}_{\lambda\mu}^\tau$       397
Function, $\tilde{\mathfrak{P}}_{\lambda\mu}^\tau$       398
Function, Bessel      147
Function, Bessel, modified      151
Function, central      106
Function, cone      324
Function, cylindrical      147 153
Function, generating      169
Function, Hankel      150
Function, homogeneous      77
Function, hypergeometric      140 144
Function, hypergeometric, confluent      144
Function, Jacobi      156
Function, Legendre      156
Function, Legendre of the first kind      156 403
Function, Legendre of the second kind      403
Function, Legendre, associated      156
Function, Macdonald      151
Function, Neumann      150
Function, parabolic cylinder      154 226
Function, rapidly decreasing      22
Function, spherical      102
Function, spherical, associated      102
Function, spherical, Whittaker      154
Function, zonal      102
Functional      13
Functional, bilinear, invariant      90
Functional, poly linear      16
Functional, sesquilinear, invariant      90
G-set      12
G-space      12
Gamma-function      130
Group      6
Group, $\tilde{SU}(1,1)$       274
Group, action of      12
Group, cyclic      7
Group, finite      6
Group, Heisenberg      50
Group, IG      37
Group, infinite      6
Group, ISO(n), ISU(n)      38
Group, Lie      38
Group, Lie, classical complex      48
Group, Lie, compact      48
Group, Lie, covering      42
Group, Lie, nilpotent      49

Group, Lie, reductive      48
Group, Lie, semisimple      48
Group, Lie, simple      48
Group, Lie, solvable      49
Group, Lie, universal covering      43
Group, linear      35
Group, O(n, $\mathbb{C}$ ), O(n), O(p,q), SO(n), SO(p,q)      36
Group, Sp(m, $\mathbb{C}$ ), Sp(m, $\mathbb{R}$ )      36
Group, Sp(p,q), Sp(n), GL(n, $\mathbb{H}$ ), SL(n, $\mathbb{H}$ ), O(m, $\mathbb{H}$ ), SO(m, $\mathbb{H}$ )      36 37
Group, SU(1,1)      269
Group, SU(1,1), invariant measure      274
Group, SU(2)      268
Group, SU(2), invariant measure      274
Group, symmetric      6
Group, U(p,q), SU(p,q), U(n), SU(n)      36
Group, U*(2m), SU*(2m), O*(2m), SO*(2m), $S_\pm(n,\mathbb{C})$ , $N_\pm(n,\mathbb{C})$       37
Homeomorphism      19
Homomorphism      11
Homomorphism of algebras      14
Homomorphism of groups      11
Hyperboloid      77
Ideal      10
Ideal, maximal      50
Ideal, two-sided      10
Identity      6
Identity, Biedenham — Elliott      358
Identity, Jacobi      8
inversion      8
Inversion, even (odd)      8
Involution      14
Isomorphism      11
Isomorphism of groups      11
Isomorphism of Lie groups, local      43
Jordan blocks      31
Kernel      11
Kernel of a homomorhism      11
Kernel of a mapping      13
Kernel of ineffectiveness      12
Lemma, Schur’s      89
Manifold      20
Manifold, analytic      20
Manifold, complex      20
Manifold, differentiable      20
Manifold, Grassman      53
Manifold, Stiffel      54
Mapping      13
Mapping, continuous      19
Mapping, exponential      42
Mapping, invertible      13
Mapping, involutive      14
Mapping, isometric      20
Mapping, trilinear      16
Matrix      8
Matrix, non-singular      8
Matrix, Pauli      14
Matrix, skew-symmetric      19
Matrix, symmetric      19
Matrix, unimodular      10
Measure      25
Measure, Haar      63
Measure, invariant      62
Measure, Lebesgue      26
Measure, relatively invariant      62
Metric      19
Motion of a plane      164
Multiplicity of a representation      107
Neighborhood      19
Neighborhood, parametrized      20
Norm      25
normalizer      10
Normalizer of a subgroup      10
Normalizer of a subring      11
Operator      27
Operator, bounded      27
Operator, Casimir      76
Operator, Casimir for $\mathfrak{su}(2)$       271
Operator, closed      27
Operator, Hermitian (self-adjoint)      27
Operator, Hilbert — Schmidt      28
Operator, infinitesimal      74
Operator, invariant      89
Operator, Laplace      76
Operator, Laplace on SU(1,1)      488
Operator, Laplace on SU(2)      370
Operator, strictly positive      27
Operator, wave, generalized      85
Operators      14
Operators, Hermitian-adjoint      27
Operators, permutable      27
Order of a group      6
Parametrization, canonical      38
Plane, pseudo-Euclidean      170
Polynomial, Charlier      264
Polynomial, Chebyshev      155
Polynomial, Chebyshev of the first kind      155 356
Polynomial, Chebyshev of the second kind      155 356
Polynomial, Eberlane      549
Polynomial, Gegenbauer      155
Polynomial, Hahn      546
Polynomial, Hahn, continuous symmetric      560
Polynomial, Hahn, dual      549
Polynomial, Hahn, dual, continuous      560
Polynomial, harmonic      85
Polynomial, Hermite      155 231
Polynomial, Jacobi      155
Polynomial, Krawtchouk      346
Polynomial, Laguerre      155 251
Polynomial, Legendre      155 294
Polynomial, Meixner      349
Polynomial, Pollaczek — Meixner      472
Polynomial, Racah      552
Polynomial, Wilson      555
PRODUCT      15
Product of groups      15
Product of groups, direct      15
Product of groups, semidirect      17
Product, scalar      26
Product, tensor      32
Product, tensor, of operators      32
Product, tensor, of representations      70
Product, tensor, of spaces      32
Radical of a group      50
Relation, Kummer      221
Representation      12 67
Representation, adjoint      67
Representation, analytic      67
Representation, completely reducible      80
Representation, continuous      67
Representation, contragradient      82
Representation, cyclic      81
Representation, faithful      67
Representation, identity (vector)      67
Representation, indecomposable      81
Representation, irreducible      80
Representation, of a group ring      72
Representation, of a Lie algebra      72
Representation, of an associative algebra      72
Representation, of class      1 102
Representation, of SU(1,1)      297
Representation, of SU(1,1), discrete series      307
Representation, of SU(1,1), integral      300
Representation, of SU(1,1), irreducible      305
Representation, of SU(1,1), unitary      307
Representation, of SU(2)      275
Representation, operator-irreducible      90
Representation, quasi-regular      77
Representation, quotient      81
Representation, real-analytic      67
Representation, reducible      80
Representation, regular      77

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