{
  "id": "math/0507243",
  "version": "v1",
  "published": "2005-07-12T19:05:50.000Z",
  "updated": "2005-07-12T19:05:50.000Z",
  "title": "Convergence of spherical averages for actions of free groups",
  "authors": [
    "Alexander I. Bufetov"
  ],
  "comment": "16 pages, published version",
  "journal": "Annals of Math. (2), Vol. 155 (2002), no. 3, 929--944",
  "categories": [
    "math.DS"
  ],
  "abstract": "Convergence of non-uniform spherical averages is obtained for measure-preserving actions of free groups. This result generalizes theorems of Grigorichuk, Nevo and Stein [in particular, a simpler proof of the Nevo-Stein theorem about uniform spherical averages is obtained.] The proof uses the Markov operator approach, first proposed by R.I. Grigorchuk. To a measure-preserving action of a free group and a matrix of weights, a Markov operator is assigned in such a way that convergence of spherical averages with corresponding weights is equivalent to convergence of powers of the Markov operator. That last is obtained using Rota's \"Alternierende Verfahren\"; the 0-2 law for Markov operators in the form of Kaimanovich; and a suitable maximal inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-07-12T19:05:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A30",
      "47A35"
    ],
    "keywords": [
      "free group",
      "convergence",
      "result generalizes theorems",
      "markov operator approach",
      "measure-preserving action"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7243B"
    }
  }
}