{
  "id": "0902.3096",
  "version": "v1",
  "published": "2009-02-18T10:54:09.000Z",
  "updated": "2009-02-18T10:54:09.000Z",
  "title": "Reconstruction of the singularities of a potential from backscattering data in 2D and 3D",
  "authors": [
    "Juan Manuel Reyes",
    "Alberto Ruiz"
  ],
  "comment": "33 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove that the singularities of a potential in the two and three dimensional Schr\\\"odinger equation are the same as the singularities of the Born approximation (Diffraction Tomography), obtained from backscattering inverse data, with an accuracy of $1/2^-$ derivative in the scale of $L^2$-based Sobolev spaces. The key point is the study of the smoothing properties of the quartic term in the Neumann-Born expansion of the scattering amplitude in 3D, together with a Leibniz formula for multiple scattering valid in any dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-18T10:54:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q40"
    ],
    "keywords": [
      "backscattering data",
      "singularities",
      "reconstruction",
      "multiple scattering valid",
      "backscattering inverse data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.3096R"
    }
  }
}