{
  "id": "math/0509057",
  "version": "v2",
  "published": "2005-09-02T22:15:07.000Z",
  "updated": "2005-11-18T18:39:55.000Z",
  "title": "The Segal-Bargmann transform for the heat equation associated with root systems",
  "authors": [
    "Gestur Olafsson",
    "Henrik Schlichtkrull"
  ],
  "comment": "Two corrections",
  "categories": [
    "math.AP"
  ],
  "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 L^2-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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-11-18T18:39:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C67"
    ],
    "keywords": [
      "heat equation",
      "segal-bargmann transform",
      "root system",
      "riemannian symmetric space g/k",
      "multiplicity function corresponds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9057O"
    }
  }
}