{
  "id": "2001.02528",
  "version": "v1",
  "published": "2020-01-08T13:57:57.000Z",
  "updated": "2020-01-08T13:57:57.000Z",
  "title": "A Liouville theorem for Lévy generators",
  "authors": [
    "Franziska Kühn"
  ],
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "Under mild assumptions, we establish a Liouville theorem for the \"Laplace\" equation $Au=0$ associated with the infinitesimal generator $A$ of a L\\'evy process: If $u$ is a weak solution to $Au=0$ which is at most of (suitable) polynomial growth, then $u$ is a polynomial. As a by-product, we obtain new regularity estimates for semigroups associated with L\\'evy processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-08T13:57:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "35B53",
      "31C05",
      "35R09",
      "60J35"
    ],
    "keywords": [
      "liouville theorem",
      "lévy generators",
      "levy process",
      "polynomial growth",
      "weak solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}