{
  "id": "1209.2779",
  "version": "v1",
  "published": "2012-09-13T04:52:25.000Z",
  "updated": "2012-09-13T04:52:25.000Z",
  "title": "Inverse backscattering for the Schrödinger equation in 2D",
  "authors": [
    "Juan Manuel Reyes"
  ],
  "doi": "10.1088/0266-5611/23/2/010",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the inverse backscattering problem for the Schr\\\"odinger equation in two dimensions. We prove that, for a non-smooth potential in 2D the main singularities up to 1/2 of the derivative of the potential are contained in the Born approximation (Diffraction Tomography approximation) constructed from the backscattering data. We measure singularities in the scale of Hilbertian Sobolev spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-13T04:52:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "schrödinger equation",
      "diffraction tomography approximation",
      "hilbertian sobolev spaces",
      "main singularities",
      "inverse backscattering problem"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007InvPr..23..625R"
    }
  }
}