{
  "id": "1911.10971",
  "version": "v1",
  "published": "2019-11-21T23:25:34.000Z",
  "updated": "2019-11-21T23:25:34.000Z",
  "title": "Formulae for the derivatives of heat semigroups",
  "authors": [
    "K. D. Elworthy",
    "Xue-Mei Li"
  ],
  "journal": "J. Funct. Anal. 125 (1994), no. 1, 252-286",
  "categories": [
    "math.PR"
  ],
  "abstract": "We use a basic martingale method to show a differentiation formula for the derivatives $$d(P_tf)(x_0)(v_0)={1\\over t} E f(x_t) \\int_0^t \\langle Y(x_s)(v_s),dB_t\\rangle_{R^m}.$$ These are proved first on $R^n$, then on manifolds. Afterwards for solutions of heat equations on differential forms, and a second order formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-21T23:25:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heat semigroups",
      "derivatives",
      "second order formula",
      "basic martingale method",
      "differential forms"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}