{
  "id": "math-ph/0604013",
  "version": "v1",
  "published": "2006-04-06T15:32:09.000Z",
  "updated": "2006-04-06T15:32:09.000Z",
  "title": "Scattering matrices and Weyl functions",
  "authors": [
    "Jussi Behrndt",
    "Mark M. Malamud",
    "Hagen Neidhardt"
  ],
  "comment": "39 pages",
  "doi": "10.1112/plms/pdn016",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "For a scattering system $\\{A_\\Theta,A_0\\}$ consisting of selfadjoint extensions $A_\\Theta$ and $A_0$ of a symmetric operator $A$ with finite deficiency indices, the scattering matrix $\\{S_\\gT(\\gl)\\}$ and a spectral shift function $\\xi_\\Theta$ are calculated in terms of the Weyl function associated with the boundary triplet for $A^*$ and a simple proof of the Krein-Birman formula is given. The results are applied to singular Sturm-Liouville operators with scalar and matrix potentials, to Dirac operators and to Schr\\\"odinger operators with point interactions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-06T15:32:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A40",
      "47A55",
      "47B25",
      "47B44",
      "47E05"
    ],
    "keywords": [
      "weyl function",
      "scattering matrices",
      "finite deficiency indices",
      "spectral shift function",
      "singular sturm-liouville operators"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}