Representation of Lie Groups and Special Functions, 1993 Volume 2: Class I Representations, Special Functions, and Integral Transforms Mathematics and its Applications Series, Vol. 74

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%.

9: Special Functions Connected with SO(n) and with Related Groups.- 10: Representations of Groups, Related to SO(n ? 1), in Non-Canonical Bases, Special Functions, and Integral Transforms.- 11: Special Functions Connected with the Groups U(n), U(0?1,1) and IU(n ? 1).- 12: Representations of the Heisenberg Group and Special Functions.- 13: Representations of the Discrete Groups and Special Functions of Discrete Argument.

Title is also available as part of a set: Representation of Lie Groups and Special Functions (978-0-7923-1494-3)