{
  "id": "1902.10215",
  "version": "v1",
  "published": "2019-02-26T20:49:12.000Z",
  "updated": "2019-02-26T20:49:12.000Z",
  "title": "Sharp Constants of Approximation Theory. III. Polynomial Inequalities of Different Metrics on Convex Sets",
  "authors": [
    "Michael I. Ganzburg"
  ],
  "comment": "17 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $V\\subset\\R^m$ be a centrally symmetric convex body and let $V^*\\subset\\R^m$ be its polar. We prove limit relations between the sharp constants in the multivariate Markov-Bernstein-Nikolskii type inequalities for algebraic polynomials on $V^*$ and the corresponding constants for entire functions of exponential type with the spectrum in $V$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-26T20:49:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A17",
      "41A63",
      "26D10"
    ],
    "keywords": [
      "sharp constants",
      "convex sets",
      "approximation theory",
      "polynomial inequalities",
      "multivariate markov-bernstein-nikolskii type inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}