{
  "id": "2403.14411",
  "version": "v1",
  "published": "2024-03-21T13:58:00.000Z",
  "updated": "2024-03-21T13:58:00.000Z",
  "title": "Rational approximation of operator semigroups via the $\\mathcal B$-calculus",
  "authors": [
    "Alexander Gomilko",
    "Yuri Tomilov"
  ],
  "comment": "This is a version of the paper to appear in Journal of Functional Analysis",
  "categories": [
    "math.FA",
    "cs.NA",
    "math.AP",
    "math.NA"
  ],
  "abstract": "We improve the classical results by Brenner and Thom\\'ee on rational approximations of operator semigroups. In the setting of Hilbert spaces, we introduce a finer regularity scale for initial data, provide sharper stability estimates, and obtain optimal approximation rates. Moreover, we strengthen a result due to Egert-Rozendaal on subdiagonal Pad\\'e approximations of operator semigroups. Our approach is direct and based on the theory of the $\\mathcal B$- functional calculus developed recently. On the way, we elaborate a new and simple approach to construction of the $\\mathcal B$-calculus thus making the paper essentially self-contai",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-21T13:58:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "operator semigroups",
      "rational approximation",
      "essentially self-contai",
      "subdiagonal pade approximations",
      "optimal approximation rates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}