{
  "id": "2105.08641",
  "version": "v2",
  "published": "2021-05-18T16:09:47.000Z",
  "updated": "2021-08-16T05:32:24.000Z",
  "title": "Second-Order Differential Operators in the Limit Circle Case",
  "authors": [
    "Dmitri R. Yafaev"
  ],
  "journal": "SIGMA 17 (2021), 077, 13 pages",
  "doi": "10.3842/SIGMA.2021.077",
  "categories": [
    "math.CA"
  ],
  "abstract": "We consider symmetric second-order differential operators with real coefficients such that the corresponding differential equation is in the limit circle case at infinity. Our goal is to construct the theory of self-adjoint realizations of such operators by an analogy with the case of Jacobi operators. We introduce a new object, the quasiresolvent of the maximal operator, and use it to obtain a very explicit formula for the resolvents of all self-adjoint realizations. In particular, this yields a simple representation for the Cauchy-Stieltjes transforms of the spectral measures playing the role of the classical Nevanlinna formula in the theory of Jacobi operators.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2021-08-16T05:32:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C45",
      "39A70",
      "47A40",
      "47B39"
    ],
    "keywords": [
      "limit circle case",
      "symmetric second-order differential operators",
      "self-adjoint realizations",
      "jacobi operators",
      "real coefficients"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}