{
  "id": "1301.2460",
  "version": "v2",
  "published": "2013-01-11T11:31:34.000Z",
  "updated": "2013-08-04T16:17:56.000Z",
  "title": "On unique continuation for Schrödinger operators of fractional and higher orders",
  "authors": [
    "Ihyeok Seo"
  ],
  "comment": "Revised version, to appear in Mathematische Nachrichten",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this note we study the property of unique continuation for solutions of $|(-\\Delta)^{\\alpha/2}u|\\leq|Vu|$, where $V$ is in a function class of potentials including $\\bigcup_{p>n/\\alpha}L^p(\\mathbb{R}^n)$ for $n-1\\leq\\alpha<n$. In particular, when $n=2$, our result gives a unique continuation theorem for the fractional ($1<\\alpha<2$) Schr\\\"odinger operator $(-\\Delta)^{\\alpha/2}+V(x)$ in the full range of $\\alpha$ values.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-08-04T16:17:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "schrödinger operators",
      "higher orders",
      "fractional",
      "unique continuation theorem",
      "function class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.2460S"
    }
  }
}