{
  "id": "math-ph/0206023",
  "version": "v1",
  "published": "2002-06-14T22:36:05.000Z",
  "updated": "2002-06-14T22:36:05.000Z",
  "title": "Sum Rules and the Szego Condition for Orthogonal Polynomials on the Real Line",
  "authors": [
    "Barry Simon",
    "Andrej Zlatos"
  ],
  "doi": "10.1007/s00220-003-0906-5",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the Case sum rules, especially $C_0$, for general Jacobi matrices. We establish situations where the sum rule is valid. Applications include an extension of Shohat's theorem to cases with an infinite point spectrum and a proof that if $\\lim n (a_n -1)=\\alpha$ and $\\lim nb_n =\\beta$ exist and $2\\alpha <\\abs{\\beta}$, then the Szeg\\H{o} condition fails.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-06-14T22:36:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B36",
      "42C05"
    ],
    "keywords": [
      "real line",
      "orthogonal polynomials",
      "szego condition",
      "case sum rules",
      "general jacobi matrices"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Commun. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}