Representation of Lie Groups and Special Functions de N.Ja. Vilenkin

Representation of Lie Groups and Special Functions: Volume 1: Simplest Lie Groups, Special Functions and Integral Transforms: Mathematics and its Applications, cartea 72

N.Ja. Vilenkin

A.U. Klimyk

en Limba Engleză Paperback – 25 sep 2012

In 1991-1993 our three-volume book "Representation of Lie Groups and Spe cial Functions" was published. When we started to write that book (in 1983), editors of "Kluwer Academic Publishers" expressed their wish for the book to be of encyclopaedic type on the subject. Interrelations between representations of Lie groups and special functions are very wide. This width can be explained by existence of different types of Lie groups and by richness of the theory of their rep resentations. This is why the book, mentioned above, spread to three big volumes. Influence of representations of Lie groups and Lie algebras upon the theory of special functions is lasting. This theory is developing further and methods of the representation theory are of great importance in this development. When the book "Representation of Lie Groups and Special Functions" ,vol. 1-3, was under preparation, new directions of the theory of special functions, connected with group representations, appeared. New important results were discovered in the traditional directions. This impelled us to write a continuation of our three-volume book on relationship between representations and special functions. The result of our further work is the present book. The three-volume book, published before, was devoted mainly to studying classical special functions and orthogonal polynomials by means of matrix elements, Clebsch-Gordan and Racah coefficients of group representations and to generaliza tions of classical special functions that were dictated by matrix elements of repre sentations.

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Paperback (4)

651^.51 lei 6-8 săpt.

SPRINGER NETHERLANDS – 7 dec 2010

651^.51 lei 6-8 săpt.

SPRINGER NETHERLANDS – 5 dec 2010

959^.98 lei 6-8 săpt.

SPRINGER NETHERLANDS – 25 sep 2012

960^.78 lei 6-8 săpt.

SPRINGER NETHERLANDS – 5 dec 2010

1397^.05 lei 6-8 săpt.

Hardback (3)

657^.90 lei 6-8 săpt.

SPRINGER NETHERLANDS – 30 noi 1994

657^.90 lei 6-8 săpt.

SPRINGER NETHERLANDS – 31 dec 1992

966^.90 lei 6-8 săpt.

SPRINGER NETHERLANDS – 30 sep 1992

1403^.67 lei 6-8 săpt.

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Specificații

ISBN-13: 9789401055666
ISBN-10: 9401055661
Pagini: 640
Ilustrații: XXIII, 612 p.
Dimensiuni: 155 x 235 x 34 mm
Greutate: 0.89 kg
Ediția:Softcover reprint of the original 1st ed. 1991
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Mathematics and its Applications

Locul publicării:Dordrecht, Netherlands

Cuprins

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.- 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.- 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.- 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).