Cover Image
Read Now

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

Bibliographic Details
Main Authors: Vilenkin, N.Ja, Klimyk, A.U. (Author)
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 1991, 1991
Edition:1st ed. 1991
Series:Mathematics and its Applications, Soviet Series
Subjects:
Special Functions
Mathematical Analysis
Harmonic Analysis
Topological Groups And Lie Groups
Lie Groups
Topological Groups
Integral Transforms And Operational Calculus
Mathematical Physics
Abstract Harmonic Analysis
Theoretical, Mathematical And Computational Physics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 5.5. Representations of the Group of Complex Third Order Triangular Matrices, Laguerre and Charlier Polynomials
  • 6: Representations of the Groups SU(2), SU(1,1) and Related Special Functions: Legendre, Jacobi, Chebyshev Polynomials and Functions, Gegenbauer, Krawtchouk, Meixner Polynomials
  • 6.1. The Groups SU(2) and SU(1,1)
  • 6.2. Finite Dimensional Irreducible Representations of the Groups GL(2,C) and SU(2)
  • 6.3. Matrix Elements of the Representations T? of the Group SL(2, C) and Jacobi, Gegenbauer and Legendre Polynomials
  • 6.4. Representations of the Group SU(1,1)
  • 6.5. Matrix Elements of Representations of SU(1, 1), Jacobi and Legendre Functions
  • 6.6. Addition Theorems and Multiplication Formulas
  • 6.7. Generating Functions and Recurrence Formulas
  • 6.8. Matrix Elements of Representations of SU(2) and SU(1,1) as Functions of Column Index. Krawtchouk and Meixner Polynomials
  • 6.9. Characters of Representations of SU(2) and Chebyshev Polynomials
  • 8.4. Racah Coefficients of SU(2) and the Hypergeometric Function 4F3(…; 1)
  • 8.5. Hahn and Racah Polynomials
  • 8.6. Clebsch-Gordan and Racah Coefficients of the Group S and Orthogonal Polynomials
  • 8.7. Clebsch-Gordan Coefficients of the Group SL(2, R)
  • 0: Introduction
  • 1: Elements of the Theory of Lie Groups and Lie Algebras
  • 1.0. Preliminary Information from Algebra, Topology, and Functional Analysis
  • 1.1. Lie Groups and Lie Algebras
  • 1.2. Homogeneous Spaces with Semisimple Groups of Motions
  • 2: Group Representations and Harmonic Analysis on Groups
  • 2.1. Representations of Lie Groups and Lie Algebras
  • 2.2. Basic Concepts of the Theory of Representations
  • 2.3. Harmonic Analysis on Groups and on Homogeneous Spaces
  • 3: Commutative Groups and Elementary Functions. The Group of Linear Transformations of the Straight Line and the Gamma-Function. Hypergeometric Functions
  • 3.1. Representations of One-Dimensional Commutative Lie Groups and Elementary Functions
  • 3.2. The Groups SO(2) and R, Fourier Series and Integrals
  • 3.3. Fourier Transform in the Complex Domain. Mellin and Laplace Transforms
  • 3.4. Representations of the Group of Linear Transforms of the Straight Line and the Gamma-Function
  • 3.5. Hypergeometric Functions and Their Properties
  • 4: Representations of the Groups of Motions of Euclidean and Pseudo-Euclidean Planes, and Cylindrical Functions
  • 4.1. Representations of the Group ISO(2) and Bessel Functions with Integral Index
  • 4.2. Representations of the Group ISO(1,1), Macdonald and Hankel Functions
  • 4.3. Functional Relations for Cylindrical Functions
  • 4.4. Quasi-Regular Representations of the Groups ISO(2), ISO(1,1) and Integral Transforms
  • 5: Representations of Groups of Third Order Triangular Matrices, the Confluent Hypergeometric Function, and Related Polynomials and Functions
  • 5.1. Representations of the Group of Third Order Real Triangular Matrices
  • 5.2. Functional Relations for Whittaker Functions
  • 5.3. Functional Relations for the Confluent Hypergeometric Function and for Parabolic Cylinder Functions
  • 5.4. Integrals Involving Whittaker Functions and Parabolic Cylinder Functions
  • 6.10. Expansion of Functions on the Group SU(2)
  • 7: Representations of the Groups SU(1,1) and SL(2,?) in Mixed Bases. The Hypergeometric Function
  • 7.1. The Realization of Representations T? in the Space of Functions on the Straight Line
  • 7.2. Calculation of the Kernels of Representations R?
  • 7.3. Functional Relations for the Hypergeometric Function
  • 7.4. Special Functions Connected with the Hypergeometric Function
  • 7.5. The Mellin Transform and Addition Formulas for the Hypergeometric Function
  • 7.6. The Kernels K33(?,?; ?; g) and Hankel Functions
  • 7.7. The Kernels Kij(?, ?; ? g), i ? j, and Special Functions
  • 7.8. Harmonic Analysis on the Group SL(2, R) and Integral Transforms
  • 8: Clebsch-GordanCoefficients, Racah Coefficients, and Special Functions
  • 8.1. Clebsch-Gordan Coefficients of the Group SU(2)
  • 8.2. Properties of CGC’s of the Group SU(2)
  • 8.3. CGC’s, the Hypergeometric Function 3F2(…; 1) and Jacobi Polynomials

Similar Items