The heat semigroup in the compact Heckman-Opdam setting and the Segal-Bargmann transform

Abstract

In the first part of this paper, we study the heat equation and the heat kernel associated with the Heckman-Opdam Laplacian in the compact, Weyl-group invariant setting. In particular, this Laplacian gives rise to a Feller-Markov semigroup on a fundamental alcove of the affine Weyl group. The second part of the paper is devoted to the Segal-Bargmann transform in our context. A Hilbert space of holomorphic functions is defined such that the $L^2$-heat transform becomes a unitary isomorphism.

18 pages

References in corpus (2)

• Fourier transforms of spherical distributions on compact symmetric spaces
• On Segal-Bargmann analysis for finite Coxeter groups and its heat kernel

Cited by in corpus (1)

• The C-version Segal-Bargmann transform for finite Coxeter groups defined by the restriction principle