{
  "id": "1709.06777",
  "version": "v1",
  "published": "2017-09-20T09:21:06.000Z",
  "updated": "2017-09-20T09:21:06.000Z",
  "title": "Estimates near the origin for functional calculus on analytic semigroups",
  "authors": [
    "I. Chalendar",
    "J. Esterle",
    "J. R. Partington"
  ],
  "comment": "17 pages, 1 figure",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "This paper provides sharp lower estimates near the origin for the functional calculus $F(-uA)$ of a generator $A$ of an operator semigroup defined on a sector; here $F$ is given as the Fourier--Borel transform of an analytic functional. The results are linked to the existence of an identity element in the Banach algebra generated by the semigroup. Both the quasinilpotent and non-quasinilpotent cases are considered, and sharp results are proved extending many in the literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-20T09:21:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47D03",
      "46J40",
      "46H30",
      "30A42",
      "47A60"
    ],
    "keywords": [
      "functional calculus",
      "analytic semigroups",
      "sharp lower estimates",
      "sharp results",
      "fourier-borel transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}