The Generalized Segal-Bargmann transform and Special Functions

Details The Generalized Segal-Bargmann transform and Special Functions The Generalized Segal-Bargmann transform and Special Functions

2003-07-25

arxiv.org/abs/math/0307343v1

Mathematics

Representation Theory

Scientific paper

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.

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