{
  "id": "0912.3129",
  "version": "v1",
  "published": "2009-12-16T13:01:23.000Z",
  "updated": "2009-12-16T13:01:23.000Z",
  "title": "A characterization of Fourier transforms",
  "authors": [
    "Philippe Jaming"
  ],
  "comment": "In memory of A. Hulanicki",
  "categories": [
    "math.CA"
  ],
  "abstract": "The aim of this paper is to show that, in various situations, the only continuous linear map that transforms a convolution product into a pointwise product is a Fourier transform. We focus on the cyclic groups $\\Z/nZ$, the integers $\\Z$, the Torus $\\T$ and the real line. We also ask a related question for the twisted convolution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-12-16T13:01:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42A38",
      "42A85",
      "42B10",
      "43A25"
    ],
    "keywords": [
      "fourier transform",
      "characterization",
      "continuous linear map",
      "convolution product",
      "cyclic groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.3129J"
    }
  }
}