{
  "id": "1307.1626",
  "version": "v1",
  "published": "2013-07-05T14:47:16.000Z",
  "updated": "2013-07-05T14:47:16.000Z",
  "title": "On convergence rates in approximation theory for operator semigroups",
  "authors": [
    "Alexander Gomilko",
    "Yuri Tomilov"
  ],
  "comment": "38 pages",
  "categories": [
    "math.FA",
    "math.AP",
    "math.NA"
  ],
  "abstract": "We create a new, functional calculus, approach to approximation of C_0-semigroups on Banach spaces. As an application of this approach, we obtain optimal convergence rates in classical approximation formulas for C_0-semigroups. In fact, our methods allow one to derive a number of similar formulas and equip them with sharp convergence rates. As a byproduct, we prove a new interpolation principle leading to efficient norm estimates in the Banach algebra of Laplace transforms of bounded measures on the semi-axis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-05T14:47:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A60",
      "65J08",
      "47D03",
      "46N40",
      "65M12"
    ],
    "keywords": [
      "approximation theory",
      "operator semigroups",
      "sharp convergence rates",
      "optimal convergence rates",
      "efficient norm estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.1626G"
    }
  }
}