{
  "id": "math/0608335",
  "version": "v1",
  "published": "2006-08-14T12:39:03.000Z",
  "updated": "2006-08-14T12:39:03.000Z",
  "title": "Image of the spectral measure of a Jacobi field and the corresponding operators",
  "authors": [
    "Yurij M. Berezansky",
    "Eugene W. Lytvynov",
    "Artem D. Pulemyotov"
  ],
  "journal": "Integral Equations Operator Theory 53 (2005), 191--208",
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "By definition, a Jacobi field $J=(J(\\phi))_{\\phi\\in H_+}$ is a family of commuting selfadjoint three-diagonal operators in the Fock space $\\mathcal F(H)$. The operators $J(\\phi)$ are indexed by the vectors of a real Hilbert space $H_+$. The spectral measure $\\rho$ of the field $J$ is defined on the space $H_-$ of functionals over $H_+$. The image of the measure $\\rho$ under a mapping $K^+:T_-\\to H_-$ is a probability measure $\\rho_K$ on $T_-$. We obtain a family $J_K$ of operators whose spectral measure is equal to $\\rho_K$. We also obtain the chaotic decomposition for the space $L^2(T_-,d\\rho_K)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-08-14T12:39:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G20",
      "60H40",
      "47B36",
      "60G51"
    ],
    "keywords": [
      "spectral measure",
      "jacobi field",
      "corresponding operators",
      "commuting selfadjoint three-diagonal operators",
      "real hilbert space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8335B"
    }
  }
}