{
  "id": "1102.5557",
  "version": "v1",
  "published": "2011-02-27T22:43:09.000Z",
  "updated": "2011-02-27T22:43:09.000Z",
  "title": "Periodicity of the spectrum of a finite union of intervals",
  "authors": [
    "Mihail N. Kolountzakis"
  ],
  "comment": "4 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "A set $\\Omega$, of Lebesgue measure 1, in the real line is called spectral if there is a set $\\Lambda$ of real numbers such that the exponential functions $e_\\lambda(x) = \\exp(2\\pi i \\lambda x)$ form a complete orthonormal system on $L^2(\\Omega)$. Such a set $\\Lambda$ is called a spectrum of $\\Omega$. In this note we present a simplified proof of the fact that any spectrum $\\Lambda$ of a set $\\Omega$ which is finite union of intervals must be periodic. The original proof is due to Bose and Madan.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-27T22:43:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B99"
    ],
    "keywords": [
      "finite union",
      "periodicity",
      "complete orthonormal system",
      "lebesgue measure",
      "real line"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.5557K"
    }
  }
}