{
  "id": "0910.5731",
  "version": "v1",
  "published": "2009-10-29T20:20:51.000Z",
  "updated": "2009-10-29T20:20:51.000Z",
  "title": "Uniqueness theorem for inverse scattering problem with non-overdetermined data",
  "authors": [
    "A. G. Ramm"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Let $q(x)$ be real-valued compactly supported sufficiently smooth function, $q\\in H^\\ell_0(B_a)$, $B_a:=\\{x: |x|\\leq a, x\\in R^3$ . It is proved that the scattering data $A(-\\beta,\\beta,k)$ $\\forall \\beta\\in S^2$, $\\forall k>0$ determine $q$ uniquely. here $A(\\beta,\\alpha,k)$ is the scattering amplitude, corresponding to the potential $q$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-29T20:20:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P25",
      "35R30",
      "81Q05"
    ],
    "keywords": [
      "inverse scattering problem",
      "uniqueness theorem",
      "non-overdetermined data",
      "compactly supported sufficiently smooth function"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/43/11/112001",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2010,
      "month": "Mar",
      "volume": 43,
      "number": 11,
      "pages": 112001
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010JPhA...43k2001R"
    }
  }
}