{
  "id": "math/0011240",
  "version": "v1",
  "published": "2000-11-28T17:51:20.000Z",
  "updated": "2000-11-28T17:51:20.000Z",
  "title": "Orthonormal bases of polynomials in one complex variable",
  "authors": [
    "D. P. L. Castrigiano",
    "W. Klopfer"
  ],
  "comment": "5 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let a sequence $(P_n)$ of polynomials in one complex variable satisfy a recurre ce relation with length growing slowlier than linearly. It is shown that $(P_n) $ is an orthonormal basis in $L^2_{\\mu}$ for some measure $\\mu$ on $\\C$, if and o ly if the recurrence is a $3-$term relation with special coefficients. The supp rt of $\\mu$ lies on a straight line. This result is achieved by the analysis of a formally normal irreducible Hessenberg operator with only finitely many nonzero entries in every row. It generalizes the classical Favard's Theorem and the Representation Theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-11-28T17:51:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A10",
      "47B15"
    ],
    "keywords": [
      "orthonormal bases",
      "polynomials",
      "recurre ce relation",
      "formally normal irreducible hessenberg operator",
      "length growing slowlier"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math.....11240C"
    }
  }
}