{
  "id": "2102.08901",
  "version": "v1",
  "published": "2021-02-17T17:49:40.000Z",
  "updated": "2021-02-17T17:49:40.000Z",
  "title": "Harmonic Analysis of Covariant Functions of Characters of Normal Subgroups",
  "authors": [
    "Arash Ghaani Farashahi"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2102.07892",
  "categories": [
    "math.FA"
  ],
  "abstract": "This paper presents a systematic study for abstract harmonic analysis on classical Banach spaces of covariant functions of characters of closed normal subgroups. Let $G$ be a locally compact group and $N$ be a closed normal subgroup of $G$. Suppose that $\\xi:N\\to\\mathbb{T}$ is a continuous character and $L_\\xi^1(G,N)$ is the $L^1$-space of all covariant functions of $\\xi$ on $G$. We showed that $L^1_\\xi(G,N)$ is isometrically isomorphic to a quotient space of $L^1(G)$. It is also proved that the dual space $L^1_\\xi(G,N)^*$ is isometrically isomorphic to $L^\\infty_\\xi(G,N)$. We then investigate some analytical aspects of the presented theory for the case of semi-direct product groups. The paper is concluded by realization of the theory in the case of some interesting examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-17T17:49:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A15",
      "43A20",
      "43A85"
    ],
    "keywords": [
      "covariant functions",
      "closed normal subgroup",
      "abstract harmonic analysis",
      "isometrically isomorphic",
      "semi-direct product groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}