{
  "id": "math/0312407",
  "version": "v1",
  "published": "2003-12-22T12:42:44.000Z",
  "updated": "2003-12-22T12:42:44.000Z",
  "title": "An uncertainty inequality for finite abelian groups",
  "authors": [
    "Roy Meshulam"
  ],
  "comment": "7 pages, no figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let G be a finite abelian group of order n. For a complex valued function f on G, let \\fht denote the Fourier transform of f. The uncertainty inequality asserts that if f \\neq 0 then |supp(f)| |supp(\\fht)| \\geq n. Answering a question of Terence Tao, the following improvement of the classical inequality is shown: Let d_1<d_2 be two consecutive divisors of n. If d_1 \\leq k=|supp(f)| \\leq d_2 then: |supp(\\fht)| \\geq \\frac{n(d_1+d_2-k)}{d_1 d_2}",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-12-22T12:42:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65T50",
      "20K01"
    ],
    "keywords": [
      "finite abelian group",
      "uncertainty inequality asserts",
      "complex valued function",
      "fourier transform",
      "terence tao"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....12407M"
    }
  }
}