{
  "id": "1310.4685",
  "version": "v2",
  "published": "2013-10-17T13:01:21.000Z",
  "updated": "2014-06-13T19:18:38.000Z",
  "title": "Asymptotic of the terms of the Gegenbauer polynomial on the unit circle and applications to the inverse of Toeplitz matrices",
  "authors": [
    "Philippe Rambour"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "The first part of this paper is devoted to the study of the orthogonal polynomial on the circle, with respect of a weight of type $f_\\alpha (\\theta) = (2\\cos \\theta- 2\\cos \\theta_0)^{2\\alpha} c_1$ with $\\theta_0 \\in ]0,\\pi[$, -1/2 <\\alpha<1/2 and c_1 a sufficiently smooth function. In a second part of the paper we obtain an asymptotic of the entries $(T_N f_\\alpha)^{-1}_{k+1,l+1}$ for sufficiently large values of $k,l$, that provides a lower bound on the eigenvalues of this matrix.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-13T19:18:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gegenbauer polynomial",
      "toeplitz matrices",
      "unit circle",
      "asymptotic",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.4685R"
    }
  }
}