{
  "id": "1407.8006",
  "version": "v2",
  "published": "2014-07-30T11:46:54.000Z",
  "updated": "2016-04-06T08:27:08.000Z",
  "title": "Volume growth, temperedness and integrability of matrix coefficients on a real spherical space",
  "authors": [
    "Friedrich Knop",
    "Bernhard Krötz",
    "Eitan Sayag",
    "Henrik Schlichtkrull"
  ],
  "comment": "Additional material of 4 pages added. To appear in J. Funct. Analysis",
  "categories": [
    "math.RT"
  ],
  "abstract": "We apply the local structure theorem and the polar decomposition to a real spherical space Z=G/H and control the volume growth on Z. We define the Harish-Chandra Schwartz space on Z. We give a geometric criterion to ensure $L^p$-integrability of matrix coefficients on Z.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-30T11:46:54.000Z",
      "comment": "20 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-04-06T08:27:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "real spherical space",
      "volume growth",
      "matrix coefficients",
      "integrability",
      "temperedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.8006K"
    }
  }
}