{
  "id": "1209.4990",
  "version": "v3",
  "published": "2012-09-22T12:27:22.000Z",
  "updated": "2012-12-09T03:13:24.000Z",
  "title": "On the eigenfunctions of the complex Ornstein-Uhlenbeck operators",
  "authors": [
    "Yong Chen",
    "Yong Liu"
  ],
  "comment": "16pages",
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "Starting from the 1-dimensional complex-valued Ornstein-Uhlenbeck process, we present two natural ways to imply the associated eigenfunctions of the 2-dimensional normal Ornstein-Uhlenbeck operators in the complex Hilbert space $L_{\\Cnum}^2(\\mu)$. We call the eigenfunctions Hermite-Laguerre-Ito polynomials. In addition, the Mehler summation formula for the complex process are shown.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-12-09T03:13:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60H07",
      "60G15"
    ],
    "keywords": [
      "complex ornstein-uhlenbeck operators",
      "mehler summation formula",
      "eigenfunctions hermite-laguerre-ito polynomials",
      "complex hilbert space",
      "normal ornstein-uhlenbeck operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.4990C"
    }
  }
}