{
  "id": "1610.00268",
  "version": "v1",
  "published": "2016-10-02T12:19:24.000Z",
  "updated": "2016-10-02T12:19:24.000Z",
  "title": "Green kernels associated with Riesz kernels",
  "authors": [
    "Bent Fuglede",
    "Natalia Zorii"
  ],
  "comment": "29 pages",
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "We study properties of the $\\alpha$-Green kernel of order $0<\\alpha\\leqslant2$ for a domain $D\\subset\\mathbb R^n$, $n\\geqslant3$. This kernel is associated with the M. Riesz kernel $|x-y|^{\\alpha-n}$, $x,y\\in\\mathbb R^n$, in a manner well known in the case $\\alpha=2$. The usual principles in potential theory are established for the $\\alpha$-Green kernel, as well as the property of consistency which allows us to prove the existence of the $\\alpha$-Green equilibrium measure for a relatively closed set in $D$ of finite $\\alpha$-Green capacity. The main tool is a generalization of H. Cartan's theory of balayage (sweeping) for the Newtonian kernel to the $\\alpha$-Riesz kernels with $0<\\alpha<2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-02T12:19:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31C15"
    ],
    "keywords": [
      "green kernel",
      "riesz kernel",
      "green equilibrium measure",
      "main tool",
      "green capacity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}