{
  "id": "math-ph/0508028",
  "version": "v1",
  "published": "2005-08-14T14:09:11.000Z",
  "updated": "2005-08-14T14:09:11.000Z",
  "title": "On the spectrum of an Hamiltonian in Fock space. Discrete spectrum Asymptotics",
  "authors": [
    "Sergio Albeverio",
    "Saidakhmat N. Lakaev",
    "Tulkin H. Rasulov"
  ],
  "categories": [
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "A model operator $H$ associated with the energy operator of a system describing three particles in interaction, without conservation of the number of particles, is considered. The precise location and structure of the essential spectrum of $H$ is described. The existence of infinitely many eigenvalues below the bottom of the essential spectrum of $H$ is proved for the case where an associated generalized Friedrichs model has a resonance at the bottom of its essential spectrum. An asymptotics for the number $N(z)$ of eigenvalues below the bottom of the essential spectrum is also established. The finiteness of eigenvalues of $H$ below the bottom of the essential spectrum is proved if the associated generalized Friedrichs model has an eigenvalue with energy at the bottom of its essential spectrum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-08-14T14:09:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q10",
      "35P20",
      "47N50"
    ],
    "keywords": [
      "discrete spectrum asymptotics",
      "essential spectrum",
      "fock space",
      "associated generalized friedrichs model",
      "eigenvalue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.ph...8028A"
    }
  }
}