{
  "id": "1602.08850",
  "version": "v1",
  "published": "2016-02-29T08:08:57.000Z",
  "updated": "2016-02-29T08:08:57.000Z",
  "title": "Spectrality and tiling by cylindric domains",
  "authors": [
    "Rachel Greenfeld",
    "Nir Lev"
  ],
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "A bounded set $\\Omega \\subset \\mathbb{R}^d$ is called a spectral set if the space $L^2(\\Omega)$ admits a complete orthogonal system of exponential functions. We prove that a cylindric set $\\Omega$ is spectral if and only if its base is a spectral set. A similar characterization is obtained of the cylindric sets which can tile the space by translations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-29T08:08:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cylindric domains",
      "spectrality",
      "cylindric set",
      "spectral set",
      "complete orthogonal system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}