Representation of Lie Groups and Special Functions Volume 2: Class I Representations, Special Functions, and Integral Transform
Representation of Lie Groups and Special Functions Volume 2: Class I Representations, Special Functions, and Integral Transforms by N. Ja. Vilenkin , A. U. Klimyk
English | PDF | 1993 | 628 Pages | ISBN : 0792314921 | 36.8 MB
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.
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