{
  "id": "1411.0162",
  "version": "v1",
  "published": "2014-11-01T19:49:18.000Z",
  "updated": "2014-11-01T19:49:18.000Z",
  "title": "Laplace operators in gamma analysis",
  "authors": [
    "D. Hagedorn",
    "Y. Kondratiev",
    "E. Lytvynov",
    "A. Vershik"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $\\mathbb K(\\mathbb R^d)$ denote the cone of discrete Radon measures on $\\mathbb R^d$. The gamma measure $\\mathcal G$ is the probability measure on $\\mathbb K(\\mathbb R^d)$ which is a measure-valued L\\'evy process with intensity measure $s^{-1}e^{-s}\\,ds$ on $(0,\\infty)$. We study a class of Laplace-type operators in $L^2(\\mathbb K(\\mathbb R^d),\\mathcal G)$. These operators are defined as generators of certain (local) Dirichlet forms. The main result of the papers is the essential self-adjointness of these operators on a set of `test' cylinder functions on $\\mathbb K(\\mathbb R^d)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-01T19:49:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "60G55",
      "60G57",
      "60G20",
      "60H40"
    ],
    "keywords": [
      "gamma analysis",
      "laplace operators",
      "discrete radon measures",
      "gamma measure",
      "cylinder functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1326058,
      "adsabs": "2014arXiv1411.0162H"
    }
  }
}