{
  "id": "1207.7203",
  "version": "v2",
  "published": "2012-07-31T10:06:51.000Z",
  "updated": "2013-02-19T02:47:47.000Z",
  "title": "Extension problem and fractional operators: semigroups and wave equations",
  "authors": [
    "J. E. Galé",
    "P. J. Miana",
    "P. R. Stinga"
  ],
  "comment": "19 pages, revised version, appendix added. To appear in Journal of Evolution Equations",
  "categories": [
    "math.AP",
    "math.CA",
    "math.FA"
  ],
  "abstract": "We extend results of Caffarelli--Silvestre and Stinga--Torrea regarding a characterization of fractional powers of differential operators via an extension problem. Our results apply to generators of integrated families of operators, in particular to infinitesimal generators of bounded $C_0$ semigroups and operators with purely imaginary symbol. We give integral representations to the extension problem in terms of solutions to the heat equation and the wave equation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-02-19T02:47:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "extension problem",
      "wave equation",
      "fractional operators",
      "semigroups",
      "heat equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.7203G"
    }
  }
}