{
  "id": "math/0209329",
  "version": "v1",
  "published": "2002-09-24T21:42:57.000Z",
  "updated": "2002-09-24T21:42:57.000Z",
  "title": "Zeros of orthogonal polynomials on the real line",
  "authors": [
    "Sergey A. Denisov",
    "Barry Simon"
  ],
  "comment": "(preliminary version)",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Let $p_n(x)$ be orthogonal polynomials associated to a measure $d\\mu$ of compact support in $R$. If $E\\not\\in supp(d\\mu)$, we show there is a $\\delta>0$ so that for all $n$, either $p_n$ or $p_{n+1}$ has no zeros in $(E-\\delta, E+\\delta)$. If $E$ is an isolated point of $supp(d\\mu)$, we show there is a $\\delta$ so that for all $n$, either $p_n$ or $p_{n+1}$ has at most one zero in $(E-\\delta, E+\\delta)$. We provide an example where the zeros of $p_n$ are dense in a gap of $supp(d\\mu)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-09-24T21:42:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05",
      "47B36"
    ],
    "keywords": [
      "real line",
      "compact support",
      "orthogonal polynomials",
      "isolated point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......9329D"
    }
  }
}