{
  "id": "1702.03873",
  "version": "v1",
  "published": "2017-02-13T16:59:43.000Z",
  "updated": "2017-02-13T16:59:43.000Z",
  "title": "Measure-geometric Laplacians for discrete distributions",
  "authors": [
    "Marc Kesseböhmer",
    "Tony Samuel",
    "Hendrik Weyer"
  ],
  "comment": "8 pages, 4 figures",
  "categories": [
    "math.DS",
    "math.FA",
    "math.SP"
  ],
  "abstract": "In 2002 Freiberg and Z\\\"ahle introduced and developed a harmonic calculus for measure-geometric Laplacians associated to continuous distributions. We show that their theory can be extended to encompass distributions with finite support and give a matrix representation for the resulting operators. In the case of a uniform discrete distribution we make use of this matrix representation to explicitly determine the eigenvalues and the eigenfunctions of the associated Laplacian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-13T16:59:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B35",
      "47G30",
      "45D05",
      "34B09",
      "35P20"
    ],
    "keywords": [
      "measure-geometric laplacians",
      "matrix representation",
      "uniform discrete distribution",
      "encompass distributions",
      "finite support"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}