{
  "id": "1605.08691",
  "version": "v1",
  "published": "2016-05-27T15:37:21.000Z",
  "updated": "2016-05-27T15:37:21.000Z",
  "title": "Stockwell-Like Frames for Sobolev Spaces",
  "authors": [
    "Ubertino Battisti",
    "Michele Berra",
    "Anita Tabacco"
  ],
  "comment": "28 pages, 8 figures",
  "categories": [
    "math.FA"
  ],
  "abstract": "We construct a family of frames describing Sobolev norm and Sobolev seminorm of the space $H^s(\\mathbb{R}^d)$. Our work is inspired by the Discrete Orthonormal Stockwell Transform introduced by R.G. Stockwell, which provides a time-frequency localized version of Fourier basis of $L^2([0,1])$. This approach is a hybrid between Gabor and Wavelet frames. We construct explicit and computable examples of these frames, discussing their properties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-27T15:37:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sobolev spaces",
      "stockwell-like frames",
      "discrete orthonormal stockwell transform",
      "wavelet frames",
      "fourier basis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}