{
  "id": "1006.0900",
  "version": "v2",
  "published": "2010-06-04T14:17:23.000Z",
  "updated": "2010-08-25T10:12:18.000Z",
  "title": "Asymptotics of the L^2 Norm of Derivatives of OPUC",
  "authors": [
    "Andrei Martinez-Finkelshtein",
    "Barry Simon"
  ],
  "comment": "36 pages, no figures. Minor corrections, to appear in the Journal of Approximation Theory",
  "categories": [
    "math.CA"
  ],
  "abstract": "We show that for many families of OPUC, one has $||\\varphi'_n||_2/n -> 1$, a condition we call normal behavior. We prove that this implies $|\\alpha_n| -> 0$ and that it holds if the sequence $\\alpha_n$ is in $\\ell^1$. We also prove it is true for many sparse sequences. On the other hand, it is often destroyed by the insertion of a mass point.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-08-25T10:12:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05",
      "34D05",
      "31A99"
    ],
    "keywords": [
      "asymptotics",
      "derivatives",
      "normal behavior",
      "sparse sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.0900M"
    }
  }
}