{
  "id": "1609.03226",
  "version": "v1",
  "published": "2016-09-11T22:42:58.000Z",
  "updated": "2016-09-11T22:42:58.000Z",
  "title": "Bounded holomorphic functional calculus for nonsymmetric Ornstein-Uhlenbeck operators",
  "authors": [
    "Andrea Carbonaro",
    "Oliver Dragičević"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We study bounded holomorphic functional calculus for nonsymmetric infinite dimensional Ornstein-Uhlenbeck operators ${\\mathscr L}$. We prove that if $-{\\mathscr L}$ generates an analytic semigroup on $L^{2}(\\gamma_{\\infty})$, then ${\\mathscr L}$ has bounded holomorphic functional calculus on $L^{r}(\\gamma_{\\infty})$, $1<r<\\infty$, in any sector of angle $\\theta>\\theta^{*}_{r}$, where $\\gamma_{\\infty}$ is the associated invariant measure and $\\theta^{*}_{r}$ the sectoriality angle of ${\\mathscr L}$ on $L^{r}(\\gamma_{\\infty})$. The angle $\\theta^{*}_{r}$ is optimal. In particular our result applies to any nondegenerate finite dimensional Ornstein-Uhlenbeck operator, with dimension-free estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-11T22:42:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded holomorphic functional calculus",
      "nonsymmetric ornstein-uhlenbeck operators",
      "nonsymmetric infinite dimensional ornstein-uhlenbeck operators",
      "nondegenerate finite dimensional ornstein-uhlenbeck operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}