{
  "id": "1611.09598",
  "version": "v1",
  "published": "2016-11-29T12:34:53.000Z",
  "updated": "2016-11-29T12:34:53.000Z",
  "title": "On the denseness of the set of scattering amplitudes",
  "authors": [
    "A. G. Ramm"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "It is proved that the set of scattering amplitudes $\\{A(\\beta, \\alpha, k)\\}_{\\forall \\alpha \\in S^2}$, known for all $\\beta\\in S^2$, where $S^2$ is the unit sphere in $\\mathbb{R}^3$, $k>0$ is fixed, $k^2$ is not a Dirichlet eigenvalue of the Laplacian in $D$, is dense in $L^2(S^2)$. Here $A(\\beta, \\alpha, k)$ is the scattering amplitude corresponding to an obstacle $D$, where $D\\subset \\mathbb{R}^3$ is a bounded domain with a boundary $S$. The boundary condition on $S$ is the Dirichlet condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-29T12:34:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35J05"
    ],
    "keywords": [
      "scattering amplitude",
      "boundary condition",
      "dirichlet eigenvalue",
      "dirichlet condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}