{
  "id": "2304.08358",
  "version": "v1",
  "published": "2023-04-17T15:17:36.000Z",
  "updated": "2023-04-17T15:17:36.000Z",
  "title": "Integral representation of functions on the circle",
  "authors": [
    "Giuliano Basso"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CA",
    "math.MG"
  ],
  "abstract": "We give a complete characterization of all real-valued functions on the unit circle $S^1$ that can be represented by integrating the intrinsic distance of $S^1$ with respect to a signed measure or probability measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-17T15:17:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integral representation",
      "complete characterization",
      "intrinsic distance",
      "unit circle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}