{
  "id": "0710.2071",
  "version": "v1",
  "published": "2007-10-10T17:11:12.000Z",
  "updated": "2007-10-10T17:11:12.000Z",
  "title": "Generalized multiresolution analyses with given multiplicity functions",
  "authors": [
    "Lawrence W. Baggett",
    "Nadia S. Larsen",
    "Kathy D. Merrill",
    "Judith A. Packer",
    "Iain Raeburn"
  ],
  "comment": "16 pages including bibliography",
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "Generalized multiresolution analyses are increasing sequences of subspaces of a Hilbert space $\\H$ that fail to be multiresolution analyses in the sense of wavelet theory because the core subspace does not have an orthonormal basis generated by a fixed scaling function. Previous authors have studied a multiplicity function $m$ which, loosely speaking, measures the failure of the GMRA to be an MRA. When the Hilbert space $\\H$ is $L^2(\\mathbb R^n)$, the possible multiplicity functions have been characterized by Baggett and Merrill. Here we start with a function $m$ satisfying a consistency condition which is known to be necessary, and build a GMRA in an abstract Hilbert space with multiplicity function $m$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-10-10T17:11:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C40",
      "47D03"
    ],
    "keywords": [
      "generalized multiresolution analyses",
      "multiplicity function",
      "abstract hilbert space",
      "wavelet theory",
      "core subspace"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.2071B"
    }
  }
}