{
  "id": "1111.7292",
  "version": "v8",
  "published": "2011-11-30T20:02:31.000Z",
  "updated": "2013-12-18T07:07:02.000Z",
  "title": "Norm convergence of multiple ergodic averages on amenable groups",
  "authors": [
    "Pavel Zorin-Kranich"
  ],
  "comment": "v8: 16 p., with improved notation and a new introduction",
  "categories": [
    "math.DS"
  ],
  "abstract": "We apply Walsh's method for proving norm convergence of multiple ergodic averages to arbitrary amenable groups. We obtain convergence in the uniform Ces\\`aro sense for their polynomial actions and for ``triangular'' averages associated to commuting homomorphic actions. The latter generalizes a result due to Bergelson, McCutcheon, and Zhang in the case of two actions.",
  "revisions": [
    {
      "version": "v8",
      "updated": "2013-12-18T07:07:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A30"
    ],
    "keywords": [
      "multiple ergodic averages",
      "apply walshs method",
      "commuting homomorphic actions",
      "proving norm convergence",
      "polynomial actions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.7292Z"
    }
  }
}