{
  "id": "1302.6529",
  "version": "v4",
  "published": "2013-02-26T18:40:28.000Z",
  "updated": "2013-10-08T13:24:55.000Z",
  "title": "Heat kernel estimates for pseudodifferential operators, fractional Laplacians and Dirichlet-to-Neumann operators",
  "authors": [
    "Heiko Gimperlein",
    "Gerd Grubb"
  ],
  "comment": "31 pages, to appear in J. Evolution Eq",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "The purpose of this article is to establish upper and lower estimates for the integral kernel of the semigroup exp(-tP) associated to a classical, strongly elliptic pseudodifferential operator P of positive order on a closed manifold. The Poissonian bounds generalize those obtained for perturbations of fractional powers of the Laplacian. In the selfadjoint case, extensions to t in C_+ are studied. In particular, our results apply to the Dirichlet-to-Neumann semigroup.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-10-08T13:24:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K08",
      "58J35",
      "58J40",
      "47D06"
    ],
    "keywords": [
      "heat kernel estimates",
      "fractional laplacians",
      "dirichlet-to-neumann operators",
      "strongly elliptic pseudodifferential operator",
      "lower estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.6529G"
    }
  }
}