{
  "id": "1210.4350",
  "version": "v3",
  "published": "2012-10-16T10:52:40.000Z",
  "updated": "2013-04-22T10:16:07.000Z",
  "title": "Asymptotic behaviour of a differential operator with a finite number of transmission conditions",
  "authors": [
    "Erdoğan Şen",
    "Oktay Mukhtarov"
  ],
  "comment": "23 pages. arXiv admin note: substantial text overlap with arXiv:1201.5494, arXiv:1202.4858, arXiv:1208.5395",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper following the same methods in [M. Kadakal, O. Sh. Mukhtarov, Sturm-Liouville problems with discontinuities at two points, Comput. Math. Appl., 54 (2007) 1367-1379] we investigate discontinuous two-point boundary value problems with eigenparameter in the boundary conditions and with transmission conditions at the finitely many points of discontinuity. A self-adjoint linear operator A is defined in a suitable Hilbert space H such that the eigenvalues of such a problem coincide with those of A. We obtain asymptotic formulas for the eigenvalues and eigenfunctions. Also we show that the eigenfunctions of A are complete in H.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-04-22T10:16:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34B27",
      "34L10",
      "34L20",
      "35R10",
      "47E05"
    ],
    "keywords": [
      "transmission conditions",
      "finite number",
      "asymptotic behaviour",
      "differential operator",
      "discontinuous two-point boundary value problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.4350S"
    }
  }
}