{
  "id": "0801.3838",
  "version": "v2",
  "published": "2008-01-24T20:39:30.000Z",
  "updated": "2009-04-17T13:08:44.000Z",
  "title": "Pseudodifferential multi-product representation of the solution operator of a parabolic equation",
  "authors": [
    "Hiroshi Isozaki",
    "Jérôme Le Rousseau"
  ],
  "comment": "Comm. Partial Differential Equations to appear (2009) 28 pages",
  "journal": "Comm. Partial Differential Equations 34, 7 (2009) 625 - 655",
  "doi": "10.1080/03605300903017330",
  "categories": [
    "math.AP"
  ],
  "abstract": "By using a time slicing procedure, we represent the solution operator of a second-order parabolic pseudodifferential equation on $\\R^n$ as an infinite product of zero-order pseudodifferential operators. A similar representation formula is proven for parabolic differential equations on a compact Riemannian manifold. Each operator in the multi-product is given by a simple explicit Ansatz. The proof is based on an effective use of the Weyl calculus and the Fefferman-Phong inequality.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-04-17T13:08:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K15",
      "35S10",
      "47G30",
      "58J35",
      "58J40"
    ],
    "keywords": [
      "pseudodifferential multi-product representation",
      "solution operator",
      "parabolic equation",
      "second-order parabolic pseudodifferential equation",
      "parabolic differential equations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.3838I"
    }
  }
}