{
  "id": "math/0104050",
  "version": "v1",
  "published": "2001-04-04T14:17:10.000Z",
  "updated": "2001-04-04T14:17:10.000Z",
  "title": "Analytic families of eigenfunctions on a reductive symmetric space",
  "authors": [
    "E. P. van den Ban",
    "H. Schlichtkrull"
  ],
  "comment": "115 pages, LaTeX",
  "journal": "Represent. Theory 5 (2001), 615--712 (electronic)",
  "categories": [
    "math.RT"
  ],
  "abstract": "The asymptotic behavior of holomorphic families of generalized eigenfunctions on a reductive symmetric space is studied. The family parameter is a complex character on the split component of a parabolic subgroup. The main result asserts that the family vanishes if a particular asymptotic coefficient does. This allows an induction of relations between families that will be applied in forthcoming work on the Plancherel and the Paley-Wiener theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-04-04T14:17:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E30",
      "22E45"
    ],
    "keywords": [
      "reductive symmetric space",
      "analytic families",
      "eigenfunctions",
      "main result asserts",
      "paley-wiener theorem"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Represent. Theory"
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 115,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......4050V"
    }
  }
}