{
  "id": "2002.09980",
  "version": "v1",
  "published": "2020-02-23T20:17:37.000Z",
  "updated": "2020-02-23T20:17:37.000Z",
  "title": "Orthogonal Systems of Spline Wavelets as Unconditional Bases in Sobolev Spaces",
  "authors": [
    "Rajula Srivastava"
  ],
  "comment": "21 pages, 1 figure",
  "categories": [
    "math.CA",
    "cs.NA",
    "math.FA",
    "math.NA"
  ],
  "abstract": "We exhibit the necessary range for which functions in the Sobolev spaces $L^s_p$ can be represented as an unconditional sum of orthonormal spline wavelet systems, such as the Battle-Lemari\\'e wavelets. We also consider the natural extensions to Triebel-Lizorkin spaces. This builds upon, and is a generalization of, previous work of Seeger and Ullrich, where analogous results were established for the Haar wavelet system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-23T20:17:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "46B15",
      "42C40"
    ],
    "keywords": [
      "sobolev spaces",
      "unconditional bases",
      "orthogonal systems",
      "orthonormal spline wavelet systems",
      "haar wavelet system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}