{
  "id": "math/0701055",
  "version": "v3",
  "published": "2007-01-02T11:29:07.000Z",
  "updated": "2011-10-24T01:17:01.000Z",
  "title": "A note on Poisson brackets for orthogonal polynomials on the unit circle",
  "authors": [
    "Irina Nenciu"
  ],
  "comment": "10 pages; the statements and proofs have been corrected and expanded, and some further comments have been added",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP",
    "math.SG",
    "nlin.SI"
  ],
  "abstract": "The connection of orthogonal polynomials on the unit circle (OPUC) to the defocusing Ablowitz-Ladik integrable system involves the definition of a Poisson structure on the space of Verblunsky coefficients. In this paper, we compute the complete set of Poisson brackets for the monic orthogonal and the orthonormal polynomials on the unit circle, as well as for the second kind polynomials and the Wall polynomials. This answers a question posed by Cantero and Simon for the case of measures with finite support. We also show that the results hold for the case of measures with periodic Verblunsky coefficients.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-10-24T01:17:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05",
      "53D17"
    ],
    "keywords": [
      "unit circle",
      "orthogonal polynomials",
      "poisson brackets",
      "periodic verblunsky coefficients",
      "second kind polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1055N"
    }
  }
}