{
  "id": "1107.0745",
  "version": "v1",
  "published": "2011-07-04T21:16:47.000Z",
  "updated": "2011-07-04T21:16:47.000Z",
  "title": "Potential theory of one-dimensional geometric stable processes",
  "authors": [
    "Tomasz Grzywny",
    "Michał Ryznar"
  ],
  "comment": "28 pages",
  "journal": "Colloq. Math. 129 (2012), 7-40",
  "categories": [
    "math.PR"
  ],
  "abstract": "The purpose of this paper is to find optimal estimates for the Green function and the Poisson kernel for a half-line and intervals of the geometric stable process with parameter $\\alpha\\in(0,2]$. This process has an infinitesimal generator of the form $-\\log(1+(-\\Delta)^{\\alpha/2})$. As an application we prove the scale invariant Harnack inequality as well as the boundary Harnack principle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-07-04T21:16:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J45"
    ],
    "keywords": [
      "one-dimensional geometric stable processes",
      "potential theory",
      "scale invariant harnack inequality",
      "boundary harnack principle",
      "infinitesimal generator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.0745G"
    }
  }
}