{
  "id": "2007.02815",
  "version": "v1",
  "published": "2020-07-06T15:20:05.000Z",
  "updated": "2020-07-06T15:20:05.000Z",
  "title": "Spectral heat content for α-stable processes in C1,1 open sets",
  "authors": [
    "Hyunchul Park",
    "Renming Song"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we study the asymptotic behavior, as $t\\downarrow 0$, of the spectral heat content $Q^{(\\alpha)}_{D}(t)$ for isotropic $\\alpha$-stable processes, $\\alpha\\in [1,2)$, in bounded $C^{1,1}$ open sets $D\\subset \\R^{d}$, $d\\geq 2$. Together with the results from \\cite{Val2017} for $d=1$ and \\cite{GPS19} for $\\alpha\\in (0,1)$, the main theorem of this paper establishes the asymptotic behavior of the spectral heat content up to the second term for all $\\alpha\\in (0,2)$ and $d\\geq1$, and resolves the conjecture raised in \\cite{Val2017}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-06T15:20:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spectral heat content",
      "open sets",
      "asymptotic behavior",
      "main theorem",
      "paper establishes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}