{
  "id": "2304.10172",
  "version": "v1",
  "published": "2023-04-20T09:17:48.000Z",
  "updated": "2023-04-20T09:17:48.000Z",
  "title": "Green function and Poisson kernel associated to root systems for annular regions",
  "authors": [
    "Chaabane Rejeb"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $\\Delta_k$ be the Dunkl Laplacian relative to a fixed root system $\\mathcal{R}$ in $\\mathbb{R}^d$, $d\\geq2$, and to a nonnegative multiplicity function $k$ on $\\mathcal{R}$. Our first purpose in this paper is to solve the $\\Delta_k$-Dirichlet problem for annular regions. Secondly, we introduce and study the $\\Delta_k$-Green function of the annulus and we prove that it can be expressed by means of $\\Delta_k$-spherical harmonics. As applications, we obtain a Poisson-Jensen formula for $\\Delta_k$-subharmonic functions and we study positive continuous solutions for a $\\Delta_k$-semilinear problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-20T09:17:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "green function",
      "annular regions",
      "poisson kernel",
      "subharmonic functions",
      "poisson-jensen formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}