{
  "id": "2007.08439",
  "version": "v1",
  "published": "2020-07-16T16:25:11.000Z",
  "updated": "2020-07-16T16:25:11.000Z",
  "title": "Sharp Constants of Approximation Theory. V. An Asymptotic Equality Related to Polynomials with Given Newton Polyhedra",
  "authors": [
    "Michael Ganzburg"
  ],
  "comment": "21 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $V\\subset\\R^m$ be a convex body, symmetric about all coordinate hyperplanes, and let $\\PP_{aV},\\, a\\ge 0$, be a set of all algebraic polynomials whose Newton polyhedra are subsets of $aV$. We prove a limit equality as $a\\to \\iy$ between the sharp constant in the multivariate Markov-Bernstein-Nikolskii type inequalities for polynomials from $\\PP_{aV}$ and the corresponding constant for entire functions of exponential type with the spectrum in $V$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-16T16:25:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A17",
      "41A63",
      "26D10"
    ],
    "keywords": [
      "newton polyhedra",
      "sharp constant",
      "asymptotic equality",
      "approximation theory",
      "multivariate markov-bernstein-nikolskii type inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}