{
  "id": "math-ph/0501024",
  "version": "v1",
  "published": "2005-01-11T18:13:53.000Z",
  "updated": "2005-01-11T18:13:53.000Z",
  "title": "On the essential and discrete spectrum of a model operator related to three-particle discrete Schrödinger operators",
  "authors": [
    "Sergio Albeverio",
    "Saidakhmat N. Lakaev",
    "Ramiza Kh. Djumanova"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "A model operator $H$ corresponding to a three-particle discrete Schr\\\"odinger operator on a lattice $\\Z^3$ is studied. The essential spectrum is described via the spectrum of two Friedrichs models with parameters $h_\\alpha(p),$ $\\alpha=1,2,$ $p \\in \\T^3=(-\\pi,\\pi]^3.$ The following results are proven: 1) The operator $H$ has a finite number of eigenvalues lying below the bottom of the essential spectrum in any of the following cases: (i) both operators $h_\\alpha(0), \\alpha=1,2,$ have a zero eigenvalue; (ii) either $h_1(0)$ or $h_2(0)$ has a zero eigenvalue. 2) The operator $H$ has infinitely many eigenvalues lying below the bottom and accumulating at the bottom of the essential spectrum, if both operators $h_\\alpha(0),\\alpha=1,2,$ have a zero energy resonance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-01-11T18:13:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q10",
      "35P20",
      "47N50"
    ],
    "keywords": [
      "three-particle discrete schrödinger operators",
      "model operator",
      "discrete spectrum",
      "essential spectrum",
      "zero eigenvalue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.ph...1024A"
    }
  }
}