{
  "id": "math-ph/0702057",
  "version": "v1",
  "published": "2007-02-16T13:20:36.000Z",
  "updated": "2007-02-16T13:20:36.000Z",
  "title": "Singularly Perturbed Self-Adjoint Operators in Scales of Hilbert spaces",
  "authors": [
    "S. Albeverio",
    "S. Kuzhel",
    "L. Nizhnik"
  ],
  "comment": "26 pages",
  "journal": "Ukrainian Math. J. 59 (2007), no. 6, 787-810",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "Finite rank perturbations of a semi-bounded self-adjoint operator A are studied in the scale of Hilbert spaces associated with A. A concept of quasi-boundary value space is used to describe self-adjoint operator realizations of regular and singular perturbations of A by the same formula. As an application the one-dimensional Schr\\\"{o}dinger operator with generalized zero-range potential is considered in the Sobolev space W^p_2(\\mathbb{R}), p\\in\\mathbb{N}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-02-16T13:20:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A10",
      "47A55"
    ],
    "keywords": [
      "singularly perturbed self-adjoint operators",
      "hilbert spaces",
      "finite rank perturbations",
      "self-adjoint operator realizations",
      "quasi-boundary value space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math.ph...2057A"
    }
  }
}