{
  "id": "0907.2447",
  "version": "v2",
  "published": "2009-07-14T20:39:41.000Z",
  "updated": "2010-03-15T13:35:18.000Z",
  "title": "Positive convolution structure for a class of Heckman-Opdam hypergeometric functions of type BC",
  "authors": [
    "Margit Rösler"
  ],
  "journal": "J. Funct. Anal. 258 (2010), 2779-2800",
  "categories": [
    "math.RT",
    "math.CA"
  ],
  "abstract": "In this paper, we derive explicit product formulas and positive convolution structures for three continuous classes of Heckman-Opdam hypergeometric functions of type $BC$. For specific discrete series of multiplicities these hypergeometric functions occur as the spherical functions of non-compact Grassmann manifolds $G/K$ over one of the (skew) fields $\\mathbb F= \\mathbb R, \\mathbb C, \\mathbb H.$ We write the product formula of these spherical functions in an explicit form which allows analytic continuation with respect to the parameters. In each of the three cases, we obtain a series of hypergroup algebras which include the commutative convolution algebras of $K$-biinvariant functions on $G$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-03-15T13:35:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C67",
      "43A90",
      "43A62",
      "33C80"
    ],
    "keywords": [
      "heckman-opdam hypergeometric functions",
      "positive convolution structure",
      "type bc",
      "specific discrete series",
      "hypergeometric functions occur"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.2447R"
    }
  }
}