{
  "id": "1712.01363",
  "version": "v1",
  "published": "2017-12-04T21:17:55.000Z",
  "updated": "2017-12-04T21:17:55.000Z",
  "title": "On construction of transmutation operators for perturbed Bessel equations",
  "authors": [
    "Vladislav V. Kravchenko",
    "Elina L. Shishkina",
    "Sergii M. Torba"
  ],
  "comment": "16 pages, 3 figures",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "A representation for the kernel of the transmutation operator relating the perturbed Bessel equation with the unperturbed one is obtained in the form of a functional series with coefficients calculated by a recurrent integration procedure. New properties of the transmutation kernel are established. A new representation of the regular solution of the perturbed Bessel equation is given presenting a remarkable feature of uniform error bound with respect to the spectral parameter for partial sums of the series. A numerical illustration of application to the solution of Dirichlet spectral problems is presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-04T21:17:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A33",
      "33C45",
      "34A25",
      "34A45",
      "34B09",
      "34B24",
      "34B30",
      "34C20",
      "34L16",
      "42C10",
      "65L05",
      "65L15"
    ],
    "keywords": [
      "perturbed bessel equation",
      "transmutation operator",
      "construction",
      "recurrent integration procedure",
      "uniform error bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}