{
  "id": "1006.5515",
  "version": "v2",
  "published": "2010-06-29T07:15:39.000Z",
  "updated": "2013-06-28T16:46:35.000Z",
  "title": "Asymptotic behavior of the Verblunsky coefficients for the OPUC with a varying weight",
  "authors": [
    "Poplavskyi Mihail"
  ],
  "comment": "28 pages",
  "journal": "J. Math. Phys. 53, 043510 (2012)",
  "doi": "10.1063/1.4705276",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We present an asymptotic analysis of the Verblunsky coefficients for the polynomials orthogonal on the unit circle with the varying weight $e^{-nV(\\cos x)}$, assuming that the potential $V$ has four bounded derivatives on $[-1,1]$ and the equilibrium measure has a one interval support. We obtain the asymptotics as a solution of the system of \"string\" equations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-28T16:46:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B52",
      "33C47",
      "02.10.De"
    ],
    "keywords": [
      "verblunsky coefficients",
      "varying weight",
      "asymptotic behavior",
      "asymptotic analysis",
      "polynomials orthogonal"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "Journal of Mathematical Physics",
      "year": 2012,
      "month": "Apr",
      "volume": 53,
      "number": 4,
      "pages": 3510
    },
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JMP....53d3510P"
    }
  }
}