{
  "id": "2107.06027",
  "version": "v1",
  "published": "2021-07-13T12:26:39.000Z",
  "updated": "2021-07-13T12:26:39.000Z",
  "title": "Weyl transform of vector-valued functions and vector measures on the phase space associated to a locally compact abelian group",
  "authors": [
    "Ritika Singhal",
    "N. Shravan Kumar"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we introduce and study the Weyl transform of functions which are integrable with respect to a vector measure on a phase space associated to a locally compact abelian group. We also study the Weyl transform of vector measures. Later, we also introduce and study the convolution of functions from $L^p$-spaces associated to a vector measure. We also study the Weyl transform of vector-valued functions and prove a vector-valued analogue of the Hausdorff-Young inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-13T12:26:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "locally compact abelian group",
      "vector measure",
      "weyl transform",
      "phase space",
      "vector-valued functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}