{
  "id": "1401.2971",
  "version": "v1",
  "published": "2014-01-13T20:18:52.000Z",
  "updated": "2014-01-13T20:18:52.000Z",
  "title": "Heat content and small time asymptotics for Schrödinger operators on $R^d$",
  "authors": [
    "Luis Acuña Valverde",
    "Rodrigo Bañuelos"
  ],
  "categories": [
    "math.PR",
    "math.CA",
    "math.SP"
  ],
  "abstract": "This paper studies the heat content} for Schr\\\"odinger operators of the fractional Laplacian $(-\\Delta)^{\\alpha/2}$, $0<\\alpha\\leq 2$ in $R^d$, $d\\geq 1$. Employing probabilistic and analytic techniques, a small time asymptotic expansion formula is given and the \"heat content invariants\" are identified. These results are new even in the case of the Laplacian, $\\alpha=2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-13T20:18:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "schrödinger operators",
      "small time asymptotic expansion formula",
      "heat content invariants",
      "fractional laplacian",
      "paper studies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.2971A"
    }
  }
}