{
  "id": "0805.0936",
  "version": "v1",
  "published": "2008-05-07T09:47:53.000Z",
  "updated": "2008-05-07T09:47:53.000Z",
  "title": "On the inverse scattering of star-shape LC-networks",
  "authors": [
    "Filippo Visco Comandini",
    "Mazyar Mirrahimi",
    "Michel Sorine"
  ],
  "comment": "6 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "The study of the scattering data for a star-shape network of LC-transmission lines is transformed into the scattering analysis of a Schr\\\"odinger operator on the same graph. The boundary conditions coming from the Kirchhoff rules ensure the existence of a unique self-adjoint extension of the mentioned Schr\\\"odinger operator. While the graph consists of a number of infinite branches and a number finite ones, all joining at a central node, we provide a construction of the scattering solutions. Under non-degenerate circumstances (different wave travelling times for finite branches), we show that the study of the reflection coefficient in the high-frequency regime must provide us with the number of the infinite branches as well as the the wave travelling times for finite ones.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-07T09:47:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A40",
      "15A29"
    ],
    "keywords": [
      "star-shape lc-networks",
      "inverse scattering",
      "wave travelling times",
      "infinite branches",
      "unique self-adjoint extension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.0936V"
    }
  }
}