{
  "id": "math-ph/0003033",
  "version": "v1",
  "published": "2000-03-26T18:13:26.000Z",
  "updated": "2000-03-26T18:13:26.000Z",
  "title": "Wavelets and Quantum Algebras",
  "authors": [
    "Andrei Ludu",
    "Martin Greiner",
    "Jerry P. Draayer"
  ],
  "comment": "27 pages Latex, 3 figure ps",
  "journal": "J. Math. Phys. {\\bf 39} (1998) 2346",
  "doi": "10.1063/1.532292",
  "categories": [
    "math-ph",
    "math.MP",
    "math.QA"
  ],
  "abstract": "Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation a non-linear, two parameter algebra. This structure can be mapped onto the quantum group $su_{q}(2)$ in one limit, and approaches a Fourier series generating algebra, in another limit. A duality between any scaling function and its corresponding non-linear algebra is obtained. Examples for the Haar and B-wavelets are worked out in detail.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-03-26T18:13:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C40",
      "65T60",
      "81R50",
      "17B37",
      "20G42",
      "03.65.Fd",
      "02.30.-f"
    ],
    "keywords": [
      "quantum algebras",
      "non-linear multi-scale processes",
      "fourier series generating algebra",
      "q-deformed algebraic structure",
      "dilation operators"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "Journal of Mathematical Physics",
      "year": 1998,
      "month": "Apr",
      "volume": 39,
      "number": 4,
      "pages": 2346
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998JMP....39.2346L"
    }
  }
}