{
  "id": "1512.00948",
  "version": "v1",
  "published": "2015-12-03T04:58:33.000Z",
  "updated": "2015-12-03T04:58:33.000Z",
  "title": "Besov spaces of self-affine lattice tilings and pointwise regularity",
  "authors": [
    "Koichi Saka"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We investigate Besov spaces of self-affine tilings of ${\\Bbb R}^{n}$ and discuss various characterizations of those Besov spaces. We see what is a finite set of functions which generates the Besov spaces from a view of multiresolution approximation on self-affine lattice tilings of ${\\Bbb R}^{n}$. Using this result we give a generalization of already known characterizations of Besov spaces given by wavelet expansion and we apply to study the pointwise H${\\ddot {\\rm o}}$lder space. Furthermore we give descriptions of scaling exponents measured by Besov spaces, and estimations of a pointwise H${\\ddot {\\rm o}}$lder exponent to compute the pointwise scaling exponent of several oscillatory functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-03T04:58:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "besov spaces",
      "self-affine lattice tilings",
      "pointwise regularity",
      "scaling exponent",
      "finite set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151200948S"
    }
  }
}