{
  "id": "0712.1366",
  "version": "v1",
  "published": "2007-12-09T21:02:03.000Z",
  "updated": "2007-12-09T21:02:03.000Z",
  "title": "An expansion for polynomials orthogonal over an analytic Jordan curve",
  "authors": [
    "Erwin Miña-Díaz"
  ],
  "comment": "15 pages, 1 figure",
  "journal": "Communications in Mathematical Physics. Vol. 285, 3:1109-1128 (2009)",
  "doi": "10.1007/s00220-008-0541-2",
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "We consider polynomials that are orthogonal over an analytic Jordan curve L with respect to a positive analytic weight, and show that each such polynomial of sufficiently large degree can be expanded in a series of certain integral transforms that converges uniformly in the whole complex plane. This expansion yields, in particular and simultaneously, Szego's classical strong asymptotic formula and a new integral representation for the polynomials inside L. We further exploit such a representation to derive finer asymptotic results for weights having finitely many singularities (all of algebraic type) on a thin neighborhood of the orthogonality curve. Our results are a generalization of those previously obtained in [7] for the case of L being the unit circle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-12-09T21:02:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E35"
    ],
    "keywords": [
      "analytic jordan curve",
      "polynomials orthogonal",
      "szegos classical strong asymptotic formula",
      "derive finer asymptotic results",
      "integral transforms"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Communications in Mathematical Physics",
      "year": 2009,
      "month": "Feb",
      "volume": 285,
      "number": 3,
      "pages": 1109
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009CMaPh.285.1109M"
    }
  }
}