{
  "id": "2501.17440",
  "version": "v1",
  "published": "2025-01-29T06:41:41.000Z",
  "updated": "2025-01-29T06:41:41.000Z",
  "title": "Heat kernel estimates for Schrödinger operators with supercritical killing potentials",
  "authors": [
    "Soobin Cho",
    "Panki Kim",
    "Renming Song"
  ],
  "comment": "57 page",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "In this paper, we study the Schr\\\"odinger operator $\\Delta-V$, where $V$ is a supercritical non-negative potential belonging to a large class of functions containing functions of the form $b|x|^{-(2+2\\beta)}$, $b, \\beta>0$. We obtain two-sided estimates on the heat kernel $p(t, x, y)$ of $\\Delta-V$, along with estimates for the corresponding Green function. Unlike the case of the fractional Schr\\\"odinger operator $-(-\\Delta)^{\\alpha/2}-V$, $\\alpha\\in (0, 2)$, with supercritical killing potential dealt with in [11], in the present case, the heat kernel $p(t, x, y)$ decays to 0 exponentially as $x$ or $y$ tends to the origin.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-29T06:41:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47D08",
      "60J35",
      "60J65",
      "35K08"
    ],
    "keywords": [
      "heat kernel estimates",
      "schrödinger operators",
      "functions containing functions",
      "large class",
      "supercritical killing potential dealt"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 57,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}