{
  "id": "2111.05913",
  "version": "v1",
  "published": "2021-11-10T20:15:17.000Z",
  "updated": "2021-11-10T20:15:17.000Z",
  "title": "An Agmon-Allegretto-Piepenbrink principle for Schroedinger operators",
  "authors": [
    "Stefano Buccheri",
    "Luigi Orsina",
    "Augusto C. Ponce"
  ],
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "We prove that each Borel function $V : \\Omega \\to [-\\infty, +\\infty]$ defined on an open subset $\\Omega \\subset \\mathbb{R}^{N}$ induces a decomposition $\\Omega = S \\cup \\bigcup_{i} D_{i}$ such that every function in $W^{1,2}_{0}(\\Omega) \\cap L^{2}(\\Omega; V^{+} dx)$ is zero almost everywhere on $S$ and existence of nonnegative supersolutions of $-\\Delta + V$ on each component $D_{i}$ yields nonnegativity of the associated quadratic form $\\int_{D_{i}} (|\\nabla \\xi|^2+V\\xi^2)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-11-10T20:15:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J10",
      "35R05",
      "46E35",
      "35B05",
      "35J15",
      "35J20"
    ],
    "keywords": [
      "schroedinger operators",
      "agmon-allegretto-piepenbrink principle",
      "open subset",
      "borel function",
      "yields nonnegativity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}