{
  "id": "math/0104093",
  "version": "v1",
  "published": "2001-04-08T05:03:44.000Z",
  "updated": "2001-04-08T05:03:44.000Z",
  "title": "Spectral and Tiling properties of the Unit Cube",
  "authors": [
    "Alex Iosevich",
    "Steen Pedersen"
  ],
  "journal": "International Math Research Notices, (1998), Number 16, pp. 819-828",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $\\Q=[0,1)^d$ denote the unit cube in $d$-dimensional Euclidean space \\Rd and let \\T be a discrete subset of \\Rd. We show that the exponentials $e_t(x):=exp(i2\\pi tx)$, $t\\in\\T$ form an othonormal basis for $L^2(\\Q)$ if and only if the translates $\\Q+t$, $t\\in\\T$ form a tiling of \\Rd.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-04-08T05:03:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unit cube",
      "tiling properties",
      "dimensional euclidean space",
      "othonormal basis",
      "discrete subset"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}