{
  "id": "2204.10017",
  "version": "v1",
  "published": "2022-04-21T10:55:57.000Z",
  "updated": "2022-04-21T10:55:57.000Z",
  "title": "An analogue of Ingham's theorem on the Heisenberg group",
  "authors": [
    "Sayan Bagchi",
    "Pritam Ganguly",
    "Jayanta Sarkar",
    "Sundaram Thangavelu"
  ],
  "comment": "26 pages. It is an updated and modified version of arXiv:2009.14230",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "We prove an exact analogue of Ingham's uncertainty principle for the group Fourier transform on the Heisenberg group. This is accomplished by explicitly constructing compactly supported functions on the Heisenberg group whose operator-valued Fourier transforms have suitable Ingham type decay and proving an analogue of Chernoff's theorem for the family of special Hermite operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-21T10:55:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A80",
      "22E25",
      "33C45",
      "26E10",
      "46E35"
    ],
    "keywords": [
      "heisenberg group",
      "inghams theorem",
      "constructing compactly supported functions",
      "suitable ingham type decay",
      "special hermite operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}