{
  "id": "1412.3096",
  "version": "v1",
  "published": "2014-12-01T18:57:48.000Z",
  "updated": "2014-12-01T18:57:48.000Z",
  "title": "N-valid trees in wavelet theory on Vilenkin groups",
  "authors": [
    "G. S. Berdnikov",
    "S. F. Lukomskii"
  ],
  "comment": "24 pages. arXiv admin note: substantial text overlap with arXiv:1303.5635",
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "We consider a class of $(N,M)$-elementary step functions on the $p$-adic Vilenkin group. We prove that $(N,M)$-elementary step function generates a MRA on $p$-adic Vilenkin group iff it is generated by a special $N$-valid rooted tree on the set of vertices $\\{0,1,\\dots p-1\\}$ with the vector $(0,...,0)\\in \\mathbb Z^N$ as a root. Bibliography: 15 titles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-01T18:57:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C40",
      "11R56",
      "43A70"
    ],
    "keywords": [
      "wavelet theory",
      "n-valid trees",
      "adic vilenkin group",
      "elementary step function generates",
      "valid rooted tree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}