{
  "id": "math/0612131",
  "version": "v1",
  "published": "2006-12-05T20:35:37.000Z",
  "updated": "2006-12-05T20:35:37.000Z",
  "title": "Square summability of variations and convergence of the transfer operator",
  "authors": [
    "Anders Johansson",
    "Anders Öberg"
  ],
  "comment": "8 pages",
  "categories": [
    "math.DS",
    "math.PR"
  ],
  "abstract": "In this paper we study the one-sided shift operator on a state space defined by a finite alphabet. Using a scheme developed by Walters [13], we prove that the sequence of iterates of the transfer operator converges under square summability of variations of the g-function, a condition which gave uniqueness of a g-measure in [7]. We also prove uniqueness of so-called G-measures, introduced by Brown and Dooley [2], under square summability of variations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-12-05T20:35:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A05",
      "28D05",
      "37A30",
      "37A60"
    ],
    "keywords": [
      "square summability",
      "variations",
      "convergence",
      "transfer operator converges",
      "state space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12131J"
    }
  }
}