{
  "id": "1402.1145",
  "version": "v2",
  "published": "2014-02-05T20:11:51.000Z",
  "updated": "2015-07-27T18:51:46.000Z",
  "title": "On a problem by Steklov",
  "authors": [
    "A. Aptekarev",
    "S. Denisov",
    "D. Tulyakov"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1308.6614. Several proofs are significantly simplified, typos fixed, references added",
  "categories": [
    "math.CA"
  ],
  "abstract": "We obtain the sharp estimates on the growth of the uniform norm of orthonormal polynomials for measures satisfying the Steklov condition. This improves the earlier results by Rakhmanov and completely settles a problem by Steklov. The sharp estimates for the polynomial entropy in the Steklov class are obtained as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-05T20:11:51.000Z",
      "comment": "arXiv admin note: text overlap with arXiv:1308.6614",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-07-27T18:51:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sharp estimates",
      "steklov condition",
      "steklov class",
      "polynomial entropy",
      "uniform norm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.1145A"
    }
  }
}