{
  "id": "math/0501450",
  "version": "v1",
  "published": "2005-01-25T15:43:13.000Z",
  "updated": "2005-01-25T15:43:13.000Z",
  "title": "An equivalent representation of the Jacobi field of a Lévy process",
  "authors": [
    "Eugene Lytvynov"
  ],
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "In [Yu.M. Berezansky, E. Lytvynov, D. A. Mierzejewski, Ukrainian Math. J. 55 (2003), 853--858 ], the Jacobi field of a L\\'evy process was derived. This field consists of commuting self-adjoint operators acting in an extended (interacting) Fock space. However, these operators have a quite complicated structure. In this note, using ideas from [L. Accardi. U. Franz, M. Skeide, Comm. Math. Phys. 228 (2002), 123--150] and [E. Lytvynov, Infin. Dimen. Anal. Quant. Prob. Rel. Top. 7 (2004), 619--629], we obtain a unitary equivalent representation of the Jacobi field of a L\\'evy process. In this representation, the operators act in a usual symmetric Fock space and have a much simpler structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-01-25T15:43:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G20",
      "60G51",
      "60H40",
      "47B36"
    ],
    "keywords": [
      "jacobi field",
      "lévy process",
      "usual symmetric fock space",
      "levy process",
      "operators act"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......1450L"
    }
  }
}