Title

Laguerre functions on symmetric cones and recursion relations in the real case

Document Type

Article

Publication Date

2-1-2007

Abstract

In this article we derive differential recursion relations for the Laguerre functions on the cone Ω of positive definite real matrices. The highest weight representations of the group Sp (n, R) play a fundamental role. Each such representation acts on a Hilbert space of holomorphic functions on the tube domain Ω + i Sym (n, R). We then use the Laplace transform to carry the Lie algebra action over to L2 (Ω, d μν). The differential recursion relations result by restricting to a distinguished three-dimensional subalgebra, which is isomorphic to sl (2, R) . © 2005 Elsevier B.V. All rights reserved.

Publication Source (Journal or Book title)

Journal of Computational and Applied Mathematics

First Page

95

Last Page

112

This document is currently not available here.

Share

COinS