{
  "id": "1909.02731",
  "version": "v1",
  "published": "2019-09-06T06:23:39.000Z",
  "updated": "2019-09-06T06:23:39.000Z",
  "title": "On the eigenvalue counting function for Schrödinger operator: some upper bounds",
  "authors": [
    "Fabio E. G. Cipriani"
  ],
  "journal": "Rend. Mat. Appl. (7). Volume 39 (2018), 257-276",
  "categories": [
    "math-ph",
    "math.AP",
    "math.FA",
    "math.MP"
  ],
  "abstract": "The aim of this work is to provide an upper bound on the eigenvalues counting function $N(\\mathbb{R}^n,-\\Delta+V,e)$ of a Sch\\\"odinger operator $-\\Delta +V$ on $\\mathbb{R}^n$ corresponding to a potential $V\\in L^{\\frac{n}{2}+\\varepsilon}(\\mathbb{R}^n,dx)$, in terms of the sum of the eigenvalues counting function of the Dirichlet integral $\\mathcal{D}$ with Dirichlet boundary conditions on the subpotential domain $\\{V< e\\}$, endowed with weighted Lebesgue measure $(V-e)_-\\cdot dx$ and the eigenvalues counting function of the absorption-to-reflection operator on the equipotential surface $\\{V=e\\}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-06T06:23:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q10"
    ],
    "keywords": [
      "eigenvalue counting function",
      "upper bound",
      "eigenvalues counting function",
      "schrödinger operator",
      "dirichlet boundary conditions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}