{
  "id": "1612.07143",
  "version": "v1",
  "published": "2016-12-15T11:05:21.000Z",
  "updated": "2016-12-15T11:05:21.000Z",
  "title": "The Malgrange-Ehrenpreis theorem for nonlocal Schrödinger operators with certain potentials",
  "authors": [
    "Woocheol Choi",
    "Yong-Cheol Kim"
  ],
  "categories": [
    "math.CA",
    "math.AP"
  ],
  "abstract": "In this paper, we prove the Malgrange-Ehrenpreis theorem for nonlocal Schr\\\"odinger operators $L_K+V$ with nonnegative potentials $V\\in L^q_{\\loc}(\\BR^n)$ for $q>\\f{n}{2s}$ with $0<s<1$ and $n\\ge 2$; that is to say, we obtain the existence of a fundamental solution $\\fe_V$ for $L_K+V$ satisfying \\begin{equation*}\\bigl(L_K+V\\bigr)\\fe_V=\\dt_0\\,\\,\\text{ in $\\BR^n$ }\\end{equation*} in the distribution sense, where $\\dt_0$ denotes the Dirac delta mass at the origin. In addition, we obtain a decay of the fundamental solution $\\fe_V$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-15T11:05:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47G20",
      "45K05",
      "47G20",
      "45K05",
      "35J60",
      "35B65",
      "35D10",
      "60J75"
    ],
    "keywords": [
      "nonlocal schrödinger operators",
      "malgrange-ehrenpreis theorem",
      "fundamental solution",
      "dirac delta mass",
      "distribution sense"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}