{
  "id": "1506.07389",
  "version": "v1",
  "published": "2015-06-04T20:39:01.000Z",
  "updated": "2015-06-04T20:39:01.000Z",
  "title": "The Relationship between $ε$-Kronecker and Sidon Sets",
  "authors": [
    "Kathryn Hare",
    "L. Thomas Ramsey"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "A subset $E$ of a discrete abelian group is called $\\epsilon $-Kronecker if all $E$-functions of modulus one can be approximated to within $\\epsilon$ by characters. $E$ is called a Sidon set if all bounded $E$-functions can be interpolated by the Fourier transform of measures on the dual group. As $\\epsilon$-Kronecker sets with $\\epsilon <2$ possess the same arithmetic properties as Sidon sets, it is natural to ask if they are Sidon. We use the Pisier net characterization of Sidonicity to prove this is true.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-04T20:39:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A46",
      "42A15",
      "42A55"
    ],
    "keywords": [
      "sidon set",
      "relationship",
      "discrete abelian group",
      "pisier net characterization",
      "dual group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150607389H"
    }
  }
}