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 non-compact 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 and J. Mitchell for spaces of complex type. © 2006 Elsevier Inc. All rights reserved.
Publication Source (Journal or Book title)
Advances in Mathematics
Ólafsson, G., & Schlichtkrull, H. (2007). The Segal-Bargmann transform for the heat equation associated with root systems. Advances in Mathematics, 208 (1), 422-437. https://doi.org/10.1016/j.aim.2006.01.014