{
  "id": "1403.7891",
  "version": "v1",
  "published": "2014-03-31T07:19:22.000Z",
  "updated": "2014-03-31T07:19:22.000Z",
  "title": "Representation of Distributions by Harmonic and Monogenic Potentials in Euclidean Space",
  "authors": [
    "Fred Brackx",
    "Hendrik De Bie",
    "Hennie De Schepper"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1210.2389",
  "categories": [
    "math.FA",
    "math.CA",
    "math.CV"
  ],
  "abstract": "In the framework of Clifford analysis, a chain of harmonic and monogenic potentials in the upper half of (m+1)-dimensional Euclidean space was recently constructed, including a higher dimensional analogue of the logarithmic function in the complex plane, and their distributional boundary values were computed. In this paper we determine these potentials in lower half-space, and investigate whether they can be extended through the boundary R^m. This is a stepping stone to the representation of a doubly infinite sequence of distributions in R^m, consisting of positive and negative integer powers of the Dirac and the Hilbert-Dirac operators, as the jump across R^m of monogenic functions in the upper and lower half-spaces, in this way providing a sequence of interesting examples of Cli?fford hyperfunctions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-31T07:19:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46F20",
      "30G35",
      "31A05"
    ],
    "keywords": [
      "euclidean space",
      "monogenic potentials",
      "representation",
      "distributions",
      "lower half-space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.7891B"
    }
  }
}