{
  "id": "math/0312212",
  "version": "v2",
  "published": "2003-12-10T19:25:34.000Z",
  "updated": "2004-03-01T19:55:26.000Z",
  "title": "A family of measures associated with iterated function systems",
  "authors": [
    "Palle E. T. Jorgensen"
  ],
  "comment": "14 pages including references. Corrections made on pp.4 and 13",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $(X,d)$ be a compact metric space, and let an iterated function system (IFS) be given on $X$, i.e., a finite set of continuous maps $\\sigma_{i}$: $ X\\to X$, $i=0,1,..., N-1$. The maps $\\sigma_{i}$ transform the measures $\\mu $ on $X$ into new measures $\\mu_{i}$. If the diameter of $ \\sigma_{i_{1}}\\circ >... \\circ \\sigma_{i_{k}}(X)$ tends to zero as $ k\\to \\infty $, and if $p_{i}>0$ satisfies $\\sum_{i}p_{i}=1$, then it is known that there is a unique Borel probability measure $\\mu $ on $X$ such that $\\mu =\\sum_{i}p_{i} \\mu_{i} \\tag{*}$. In this paper, we consider the case when the $p_{i}$s are replaced with a certain system of sequilinear functionals. This allows us to study the variable coefficient case of (*), and moreover to understand the analog of (*) which is needed in the theory of wavelets.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-03-01T19:55:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42A16",
      "42A65",
      "46L45"
    ],
    "keywords": [
      "iterated function system",
      "unique borel probability measure",
      "compact metric space",
      "finite set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....12212J"
    }
  }
}