{
  "id": "1707.04163",
  "version": "v1",
  "published": "2017-07-13T15:09:08.000Z",
  "updated": "2017-07-13T15:09:08.000Z",
  "title": "Laplace-type representation for some generalized spherical functions of type BC",
  "authors": [
    "P. Sawyer"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "In [M. R\\\"osler and M. Voit. Integral Representation and Uniform Limits for Some Heckman-Opdam Hypergeometric Functions of type BC, Transactions of the American Mathematical Society, Vol. 368, No. 8, 6005-6032, 2016.], R\\\"osler and Voit give a formula for generalized spherical functions of type $BC$ in terms of the spherical functions of type A. We use this formula to describe precisely the support of the associated generalized Abel transform. Furthermore, we derive a similar formula for the generalized spherical functions in the rational Dunkl setting. The support of the intertwining operator V is also deduced. We also show, as a consequence, that a Laplace-type expression exists for the generalized spherical functions both in the trigonometric Dunkl setting and in the rational Dunkl setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-13T15:09:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C67",
      "43A90",
      "33C80",
      "43A85"
    ],
    "keywords": [
      "generalized spherical functions",
      "type bc",
      "laplace-type representation",
      "rational dunkl setting",
      "heckman-opdam hypergeometric functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}