{
  "id": "2007.07034",
  "version": "v1",
  "published": "2020-07-14T13:44:38.000Z",
  "updated": "2020-07-14T13:44:38.000Z",
  "title": "The Landis conjecture on exponential decay",
  "authors": [
    "A. Logunov",
    "E. Malinnikova",
    "N. Nadirashvili",
    "F. Nazarov"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.CA",
    "math.MP"
  ],
  "abstract": "Consider a solution $u$ to $\\Delta u +Vu=0$ on $\\mathbb{R}^2$, where $V$ is real-valued, measurable and $|V|\\leq 1$. If $|u(x)| \\leq \\exp(-C |x| \\log^{1/2}|x|)$, $|x|>2$, where $C$ is a sufficiently large absolute constant, then $u\\equiv 0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-14T13:44:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exponential decay",
      "landis conjecture",
      "sufficiently large absolute constant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}