{
  "id": "2211.06613",
  "version": "v1",
  "published": "2022-11-12T09:25:25.000Z",
  "updated": "2022-11-12T09:25:25.000Z",
  "title": "Localization Operator and Weyl Transform on Reduced Heisenberg Group with Multi-dimensional Center",
  "authors": [
    "Aparajita Dasgupta",
    "Santosh Kumar Nayak"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this article, we study two different types of operators, the localization operator and Weyl transform, on the reduced Heisenberg group with multidimensional center $\\mathcal{G}$. The group $\\mathcal{G}$ is a quotient group of non-isotropic Heisenberg group with multidimensional center $\\mathcal{H}^m$ by its center subgroup. Firstly, we define the localization operator using a wavelet transform on $\\mathcal{G}$ and obtain the product formula for the localization operators. Next, we define the Weyl transform associated to the Wigner transform on $\\mathcal{G}$ with the operator-valued symbol. Finally, we have shown that the Weyl transform is not only a bounded operator but also a compact operator when the operator-valued symbol is in $L^p,1\\leq p\\leq 2,$ and it is an unbounded operator when $p>2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-12T09:25:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47G10",
      "47G30",
      "42C40"
    ],
    "keywords": [
      "weyl transform",
      "reduced heisenberg group",
      "localization operator",
      "multi-dimensional center",
      "multidimensional center"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}