{
  "id": "math-ph/0011035",
  "version": "v3",
  "published": "2000-11-20T15:47:42.000Z",
  "updated": "2001-03-28T20:17:16.000Z",
  "title": "A non-overdetermined inverse problem of finding the potential from the spectral function",
  "authors": [
    "A. G. Ramm"
  ],
  "comment": "14pp",
  "categories": [
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "Let $D\\subset \\R^n$, $n\\geq 3,$ be a bounded domain with a $C^{\\infty}$ boundary $S$, $L=-\\nabla^2+q(x)$ be a selfadjoint operator defined in $H=L^2(D)$ by the Neumann boundary condition, $\\theta(x,y,\\lambda)$ be its spectral function, $\\theta(x,y,\\lambda):=\\ds\\sum_{\\lambda_j<\\lambda} \\phi_j(x)\\phi$ where $L\\phi_j=\\lambda_j\\phi_j$, $\\phi_{j N}|_S=0,$ $\\|\\phi_j\\|_{L^2(D)}=1$, $j=1,2,...$. The potential $q(x)$ is a real-valued function, $q\\in C^\\infty(D)$. It is proved that $q(x)$ is uniquely determined by the data $\\theta(s,s,\\lambda) \\forall s\\in S$, $\\forall \\lambda\\in \\R_+$ if all the eigenvalues of $L$ are simple.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2001-03-28T20:17:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30"
    ],
    "keywords": [
      "non-overdetermined inverse problem",
      "spectral function",
      "neumann boundary condition",
      "bounded domain",
      "selfadjoint operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math.ph..11035R"
    }
  }
}