{
  "id": "0802.3432",
  "version": "v2",
  "published": "2008-02-23T09:26:15.000Z",
  "updated": "2008-06-28T16:35:29.000Z",
  "title": "An operator approach to multipoint Pade approximations",
  "authors": [
    "Maxim S. Derevyagin",
    "Alexei S. Zhedanov"
  ],
  "comment": "18 pages",
  "categories": [
    "math.CA",
    "math.CV",
    "math.SP"
  ],
  "abstract": "First, an abstract scheme of constructing biorthogonal rational systems related to some interpolation problems is proposed. We also present a modification of the famous step-by-step process of solving the Nevanlinna-Pick problems for Nevanlinna functions. The process in question gives rise to three-term recurrence relations with coefficients depending on the spectral parameter. These relations can be rewritten in the matrix form by means of two Jacobi matrices. As a result, a convergence theorem for multipoint Pad\\'e approximants to Nevanlinna functions is proved.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-06-28T16:35:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30E05",
      "41A21",
      "47B36",
      "30E10",
      "40A15",
      "47A57"
    ],
    "keywords": [
      "multipoint pade approximations",
      "operator approach",
      "biorthogonal rational systems",
      "nevanlinna functions",
      "multipoint pade approximants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.3432D"
    }
  }
}