Representation of Lie groups and special functions / by N.Ja. Vilenkin and A.U. Klimyk ; [translated from the Russian by V.A. Groza and A.A. Groza].

Format:

Book

Author/Creator:

Vilenkin, N. I︠A︡. (Naum I︠A︡kovlevich)

Contributor:

Klimyk, A. U. (Anatoliĭ Ulʹi︠a︡novich), 1939-

Series:

Mathematics and its applications (Kluwer Academic Publishers). Soviet series ; 72, etc.

Mathematics and its applications. Soviet series ; v. 72, v. 74, v. 75

Language:

English

Russian

Subjects (All):

Representations of groups.

Lie groups.

Functions, Special.

Integral transforms.

Physical Description:

3 volumes : illustrations ; 25 cm.

Place of Publication:

Dordrecht ; Boston : Kluwer Academic Publishers, 1991-c1992.

Summary:

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.

Contents:

v. 1. Simplest Lie groups, special funtions, and integral transforms

v. 2. Class I representations, special functions, and integral transformations

v. 3. Classical and quantum groups and special functions.

Notes:

Includes bibliographical references and indexes.

ISBN:

0792314662

0792314948

OCLC:

24430261