{
  "id": "1909.06484",
  "version": "v1",
  "published": "2019-09-13T23:18:43.000Z",
  "updated": "2019-09-13T23:18:43.000Z",
  "title": "The scattering matrix for 0th order pseudodifferential operators",
  "authors": [
    "Jian Wang"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We use microlocal radial estimates to prove the full limiting absorption principle for $P$, a self-adjoint 0th order pseudodifferential operator satisfying hyperbolic dynamical assumptions as of Colin de Verdi\\`ere and Saint-Raymond. We define the scattering matrix for $P-\\omega$ when $\\omega$ is not an embedded eigenvalue of $P$ and show that the scattering matrix extends to a unitary operator on appropriate $L^2$ spaces. The operator $P$ gives microlocal model of internal waves in stratified fluids as illustrated in the paper of Colin de Verdi\\`ere and Saint-Raymond.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-13T23:18:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "scattering matrix",
      "pseudodifferential operator satisfying hyperbolic",
      "order pseudodifferential operator satisfying",
      "satisfying hyperbolic dynamical assumptions",
      "operator satisfying hyperbolic dynamical"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}