{
  "id": "1510.07019",
  "version": "v1",
  "published": "2015-10-23T19:24:01.000Z",
  "updated": "2015-10-23T19:24:01.000Z",
  "title": "Dispersion Estimates for the Discrete Laguerre Operator",
  "authors": [
    "Aleksey Kostenko",
    "Gerald Teschl"
  ],
  "comment": "8 pages",
  "categories": [
    "math-ph",
    "math.AP",
    "math.CA",
    "math.MP"
  ],
  "abstract": "We derive an explicit expression for the kernel of the evolution group $\\exp(-\\mathrm{i} t H_0)$ of the discrete Laguerre operator $H_0$ (i.e. the Jacobi operator associated with the Laguerre polynomials) in terms of Jacobi polynomials. Based on this expression we show that the norm of the evolution group acting from $\\ell^1$ to $\\ell^\\infty$ is given by $(1+t^2)^{-1/2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-23T19:24:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q41",
      "47B36",
      "81U30",
      "81Q05"
    ],
    "keywords": [
      "discrete laguerre operator",
      "dispersion estimates",
      "explicit expression",
      "jacobi polynomials",
      "jacobi operator"
    ],
    "publication": {
      "doi": "10.1007/s11005-016-0831-0",
      "journal": "Letters in Mathematical Physics",
      "year": 2016,
      "month": "Apr",
      "volume": 106,
      "number": 4,
      "pages": 545
    },
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016LMaPh.106..545K"
    }
  }
}