{
  "id": "1907.08144",
  "version": "v1",
  "published": "2019-07-18T16:28:14.000Z",
  "updated": "2019-07-18T16:28:14.000Z",
  "title": "Functional model for boundary value problems and its application to the spectral analysis of transmission problems",
  "authors": [
    "Kirill D. Cherednichenko",
    "Alexander V. Kiselev",
    "Luis O. Silva"
  ],
  "comment": "33 pages",
  "categories": [
    "math.AP",
    "cond-mat.mtrl-sci",
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We provide explicit formulae for the resolvents of the associated extensions of symmetric operators in terms of the associated generalised Dirichlet-to-Neumann maps, which can be utilised in the analysis of the properties of parameter-dependent problems as well as in the study of their spectra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-18T16:28:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A45",
      "34L25",
      "81Q35"
    ],
    "keywords": [
      "boundary value problems",
      "functional model",
      "spectral analysis",
      "transmission problems",
      "application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}