{
  "id": "math/0703349",
  "version": "v2",
  "published": "2007-03-12T16:36:58.000Z",
  "updated": "2007-09-07T15:12:20.000Z",
  "title": "Equivalence of A-Approximate Continuity for Self-Adjoint Expansive Linear Maps",
  "authors": [
    "Angel San Antolin",
    "Szilárd Gy. Révész"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Let A be an expansive linear map from R^d to R^d. The notion of A-approximate continuity was recently used to give a characterization of scaling functions in a multiresolution analysis (MRA). The definition of A-approximate continuity at a point x - or, equivalently, the definition of the family of sets having x as point of A-density - depend on the expansive linear map A. The aim of the present paper is to characterize those self-adjoint expansive linear maps A_1, A_2 for which the respective concepts of A_j-approximate continuity (j=1,2) coincide. These we apply to analyze the equivalence among dilation matrices for a construction of systems of MRA. In particular, we give a full description for the equivalence class of the dyadic dilation matrix among all self-adjoint expansive maps. If the so-called ``four exponentials conjecture'' of algebraic number theory holds true, then a similar full description follows even for general self-adjoint expansive linear maps, too.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-09-07T15:12:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A04",
      "42C40"
    ],
    "keywords": [
      "a-approximate continuity",
      "equivalence",
      "algebraic number theory holds true",
      "general self-adjoint expansive linear maps",
      "full description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3349S"
    }
  }
}