Representation of Lie Groups and Special Functions: Volume 2: Class I Representations, Special Functions, and Integral Transforms

Representation of Lie Groups and Special Functions

by Naum Yakovlevich Vilenkin, A.U. Klimyk

This is the second 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 special functions and orthogonal polynomials (Legendre, Gegenbauer, Jacobi, Laguerre, Bessel and others) which are related to the class 1 representations of various groups. The tree method for the construction of bases for representation spaces is given. `Continuous' bases in the spaces of functions on hyperboloids and cones and corresponding Poisson kernels are found. Also considered are the properties of the q-analogs of classical orthogonal polynomials, related to representations of the Chevalley groups and of special functions connected with fields of p-adic numbers. Much of the material included appears in book form for the first time and many of the topics are presented in a novel way. This volume will be of great interest to specialists in group representations, special functions, differential equations with partial derivatives and harmonic anlysis. Subscribers to the complete set of three volumes will be entitled to a discount of 15%.

626 pages, Paperback

First published December 11, 1992

About the author

Naum Yakovlevich Vilenkin (Russian: Наум Яковлевич Виленкин, October 30, 1920 in Moscow – October 19, 1991 in Moscow) was a Soviet mathematician, an expert in representation theory, the theory of special functions, functional analysis, and combinatorics. He is best known as the author of many books in recreational mathematics aimed at middle and high school students.