The Segal-Bargmann transform for the heat equation associated with root systems

2005/09/02 by Gestur Olafsson, Olafsson, Gestur, Henrik Schlichtkrull +1
Mathematics · #33C67 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:33C67

paper · pdf · doi:10.48550/arxiv.math/0509057

Two corrections

arxiv created 2005/11/18 · arxiv updated 2009/12/01

Abstract

We study the heat equation associated to a multiplicity function on a root system, where the corresponding Laplace operator has been defined by Heckman and Opdam. In particular, we describe the image of the associated Segal-Bargmann transform as a space of holomorphic functions. In the case where the multiplicity function corresponds to a Riemannian symmetric space G/K of noncompact type, we obtain a description of the image of the space of K-invariant L²-function on G/K under the Segal-Bargmann transform associated to the heat equation on G/K, thus generalizing (and reproving) a result of B. Hall for spaces of complex type.

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