{
  "id": "2210.08314",
  "version": "v1",
  "published": "2022-10-15T15:07:27.000Z",
  "updated": "2022-10-15T15:07:27.000Z",
  "title": "Quantum harmonic analysis on locally compact groups",
  "authors": [
    "Simon Halvdansson"
  ],
  "categories": [
    "math.FA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "On a locally compact group we introduce covariant quantization schemes and analogs of phase space representations as well as mixed-state localization operators. These generalize corresponding notions for the affine group and the Heisenberg group. The approach is based on associating to a square integrable representation of the locally compact group two types of convolutions between integrable functions and trace class operators. In the case of non-unimodular groups these convolutions only are well-defined for admissible operators, which is an extension of the notion of admissible wavelets as has been pointed out recently in the case of the affine group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-15T15:07:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "locally compact group",
      "quantum harmonic analysis",
      "affine group",
      "covariant quantization schemes",
      "trace class operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}