{
  "id": "1008.0163",
  "version": "v1",
  "published": "2010-08-01T10:34:29.000Z",
  "updated": "2010-08-01T10:34:29.000Z",
  "title": "Haar bases for $L^2(\\mathbb{Q}_2^2)$ generated by one wavelet function",
  "authors": [
    "S. Albeverio",
    "M. Skopina"
  ],
  "comment": "19 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "The concept of $p$-adic quincunx Haar MRA was introduced and studied in~\\cite{KS10}. In contrast to the real setting, infinitely many different wavelet bases are generated by a $p$-adic MRA. We give an explicit description for all wavelet functions corresponding to the quincunx Haar MRA. Each one generates an orthogonal basis, one of them was presented in~\\cite{KS10}. A connection between quincunx Haar bases and two-dimensional separable Haar MRA is also found.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-01T10:34:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C40",
      "11E95",
      "11F85"
    ],
    "keywords": [
      "wavelet function",
      "adic quincunx haar mra",
      "two-dimensional separable haar mra",
      "quincunx haar bases",
      "wavelet bases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.0163A"
    }
  }
}