Representation of Lie Groups and Special Functions Volume 1: Simplest Lie Groups, Special Functions and Integral Transforms
Main Authors: | , |
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Format: | eBook |
Language: | English |
Published: |
Dordrecht
Springer Netherlands
1991, 1991
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Edition: | 1st ed. 1991 |
Series: | Mathematics and its Applications, Soviet Series
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Subjects: | |
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