{
  "id": "1210.2389",
  "version": "v1",
  "published": "2012-10-07T11:43:27.000Z",
  "updated": "2012-10-07T11:43:27.000Z",
  "title": "Distributional Boundary Values of Harmonic Potentials in Euclidean Half-space as Fundamental Solutions of Convolution Operators in Clifford Analysis",
  "authors": [
    "Fred Brackx",
    "Hendrik De Bie",
    "Hennie De Schepper"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1210.2044",
  "categories": [
    "math.CA"
  ],
  "abstract": "In the framework of Clifford analysis, a chain of harmonic and monogenic potentials in the upper half of Euclidean space $\\mR^{m+1}$ was recently constructed, including a higher dimensional analogue of the logarithmic function in the complex plane. In this construction the distributional limits of these potentials at the boundary $\\mR^{m}$ are crucial. The remarkable relationship between these distributional boundary values and four basic pseudodifferential operators linked with the Dirac and Laplace operators is studied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-07T11:43:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30G35",
      "31C45"
    ],
    "keywords": [
      "distributional boundary values",
      "clifford analysis",
      "harmonic potentials",
      "convolution operators",
      "fundamental solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.2389B"
    }
  }
}