{
  "id": "0812.2050",
  "version": "v3",
  "published": "2008-12-10T23:19:33.000Z",
  "updated": "2010-02-11T21:28:17.000Z",
  "title": "Multipoint Schur algorithm and orthogonal rational functions: convergence properties, I",
  "authors": [
    "L. Baratchart",
    "S. Kupin",
    "V. Lunot",
    "M. Olivi"
  ],
  "comment": "a preliminary version, 39 pages; some changes in the Introduction, Section 5 (Szeg\\H o type asymptotics) is extended",
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "Classical Schur analysis is intimately connected to the theory of orthogonal polynomials on the circle [Simon, 2005]. We investigate here the connection between multipoint Schur analysis and orthogonal rational functions. Specifically, we study the convergence of the Wall rational functions via the development of a rational analogue to the Szeg\\H o theory, in the case where the interpolation points may accumulate on the unit circle. This leads us to generalize results from [Khrushchev,2001], [Bultheel et al., 1999], and yields asymptotics of a novel type.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-02-11T21:28:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30B70",
      "41A20"
    ],
    "keywords": [
      "orthogonal rational functions",
      "multipoint schur algorithm",
      "convergence properties",
      "multipoint schur analysis",
      "wall rational functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.2050B"
    }
  }
}