{
  "id": "0906.3266",
  "version": "v1",
  "published": "2009-06-17T18:10:54.000Z",
  "updated": "2009-06-17T18:10:54.000Z",
  "title": "Convergence of Polynomial Ergodic Averages of Several Variables for some Commuting Transformations",
  "authors": [
    "Michael C. R. Johnson"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $(X,\\mathcal{B},\\mu)$ be a probability space and let $T_1,..., T_l$ be $l$ commuting invertible measure preserving transformations \\linebreak of $X$. We show that if $T_1^{c_1} ... T_l^{c_l}$ is ergodic for each $(c_1,...,c_l)\\neq (0,...,0)$, then the averages $\\frac{1}{|\\Phi_N|}\\sum_{u\\in\\Phi_N}\\prod_{i=1}^r T_1^{p_{i1}(u)}... T_l^{p_{il}(u)}f_i$ converge in $L^2(\\mu)$ for all polynomials $p_{ij}\\colon \\mathbb{Z}^d\\to\\mathbb{Z}$, all $f_i\\in L^{\\infty}(\\mu)$, and all F{\\o}lner sequences $\\{\\Phi_N\\}_{N=1}^{\\infty}$ in $\\mathbb{Z}^d$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-06-17T18:10:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polynomial ergodic averages",
      "commuting transformations",
      "convergence",
      "probability space",
      "commuting invertible measure preserving transformations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.3266J"
    }
  }
}