{
  "id": "2007.01119",
  "version": "v1",
  "published": "2020-07-02T14:15:15.000Z",
  "updated": "2020-07-02T14:15:15.000Z",
  "title": "Convergence of weighted ergodic averages",
  "authors": [
    "Ahmad Darwiche",
    "Dominique Schneider"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $(X, \\mathcal{A},\\mu)$ be a probability space and let $T$ be a contraction on $L^2(\\mu)$. We provide suitable conditions over sequences $(w_k)$, $(u_k)$ and $(A_k)$ in such a way that the weighted ergodic limit $\\lim\\limits_{N\\rightarrow\\infty}\\frac{1}{A_N}\\sum_{k=0}^{N-1} w_k T^{u_k}(f)=0$ $\\mu$-a.e. for any function $f$ in $L^2(\\mu)$. As a consequence of our main theorems, we also deal with the so-called one-sided weighted ergodic Hilbert transforms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-02T14:15:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weighted ergodic averages",
      "convergence",
      "one-sided weighted ergodic hilbert transforms",
      "probability space",
      "weighted ergodic limit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}