{
  "id": "math/0308131",
  "version": "v1",
  "published": "2003-08-14T02:09:36.000Z",
  "updated": "2003-08-14T02:09:36.000Z",
  "title": "An analogue of Bratteli-Jorgensen loop group actions for GMRA's",
  "authors": [
    "L. W. Baggett",
    "P. E. T. Jorgensen",
    "K. D. Merrill",
    "J. A. Packer"
  ],
  "comment": "15 pages; AMS-LaTeX; submitted to proceedings of AMS Special Session on Wavelets, Frames, and Operator Theory held at Baltimore",
  "journal": "Wavelets, Frames, and Operator Theory (College Park, Maryland, January 15-21, 2003) (C. Heil, P.E.T. Jorgensen, and D. Larson, eds.), Contemp. Math., vol. 345, American Mathematical Society, Providence, RI, 2004, pp. 11-25",
  "categories": [
    "math.OA",
    "math.CA"
  ],
  "abstract": "Several years ago, O. Bratelli and P. Jorgensen developed the concept of m-systems of filters for dilation by a positive integer N>1 on L^2(R). They constructed a loop group action on m-systems. By work of Mallat and Meyer, these m-systems are important in constructing multi-resolution analyses and wavelets associated to dilation by N and translation by Z on L^2(R). In this paper, we discuss an extension of this loop-group construction to generalized filter systems, which we will call ``M-systems,'' associated with generalized multiresolution analyses. In particular, we show that every multiplicity function has an associated generalized loop group which acts freely and transitively on the set of M-systems corresponding to the multiplicity function. The results of Bratteli and Jorgensen correspond to the case where the multiplicity function is identically equal to 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-08-14T02:09:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C40",
      "14E20",
      "46E25",
      "20C20"
    ],
    "keywords": [
      "bratteli-jorgensen loop group actions",
      "multiplicity function",
      "correspond",
      "loop-group construction",
      "generalized filter systems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......8131B"
    }
  }
}