{
  "id": "2107.02832",
  "version": "v1",
  "published": "2021-07-06T18:27:23.000Z",
  "updated": "2021-07-06T18:27:23.000Z",
  "title": "On asymptotics for $C_0$-semigroups",
  "authors": [
    "Marat V. Markin"
  ],
  "comment": "Written based on the part of arXiv:2002.09087v5 on asymptotics for semigroups, removed from arXiv:2002.09087, with new and modified statements. There is a text overlap with arXiv:2002.09087 in the Preliminaries section containing introductory information, definitions, and general remarks. arXiv admin note: substantial text overlap with arXiv:2002.09087",
  "categories": [
    "math.FA",
    "math.DS",
    "math.SP"
  ],
  "abstract": "We generalize to $C_0$-semigroups of scalar type spectral operators on complex Banach spaces the spectral bound equal growth bound condition along with a generalized Lyapunov stability theorem, known to hold for $C_0$-semigroups of normal operators on complex Hilbert spaces. For such semigroups, we obtain exponential estimates with the best stability constants. We also extend to a Banach space setting a celebrated characterization of uniform exponential stability for $C_0$-semigroups on complex Hilbert spaces and thereby acquire a characterization of uniform exponential stability for scalar type spectral and eventually norm-continuous $C_0$-semigroups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-06T18:27:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B40",
      "47B15",
      "47D03",
      "47D06",
      "47D60"
    ],
    "keywords": [
      "semigroups",
      "uniform exponential stability",
      "complex hilbert spaces",
      "bound equal growth bound condition",
      "spectral bound equal growth bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}