The Generalized Segal–Bargmann Transform and Special Functions: Representations of Lie groups, harmonic analysis on homogeneous spaces and quantization (Edited by G. Van Dijk and V.F. Molchanov)
Source: Acta Applicandae Mathematicae, Volume 81, Number 1, March 2004 , pp. 29-50(22)
Abstract:Analysis of function spaces and special functions are closely related to the representation theory of Lie groups. We explain here the connection between the Laguerre functions, the Laguerre polynomials, and the Meixner–Pollacyck polynomials on the one side, and highest weight representations of Hermitian Lie groups on the other side. The representation theory is used to derive differential equations and recursion relations satisfied by those special functions.
Keywords: Laguerre functions and polynomials; Laplace transform; Meixner–Pollacyck polynomials; bounded symmetric domains; highest weight representations; holomorphic discrete series; orthogonal polynomials; real bounded symmetric domains
Document Type: Research Article
Affiliations: 1: Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A., Email: email@example.com 2: Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A., Email: firstname.lastname@example.org
Publication date: March 2004