{
  "id": "2005.11230",
  "version": "v1",
  "published": "2020-05-22T15:07:31.000Z",
  "updated": "2020-05-22T15:07:31.000Z",
  "title": "$Γ$-supercyclicity of families of translates in weighted $L^p$-spaces on locally compact groups",
  "authors": [
    "Arafat Abbar",
    "Yulia Kuznetsova"
  ],
  "categories": [
    "math.FA",
    "math.DS"
  ],
  "abstract": "Let $\\omega$ be a weight function defined on a locally compact group $G$, $1\\le p<+\\infty$, $S\\subset G$ and let us assume that for any $s\\in S$, the left translation operator $T_s$ is continuous from the weighted $L^p$-space $L^p(G,\\omega)$ into itself. For a given set $\\Gamma\\subset\\mathbb{C}$, a vector $f\\in L^p(G,\\omega)$ is said to be $(\\Gamma,S)$-dense if the set $\\{ \\lambda T_sf:\\, \\lambda\\in \\Gamma, \\,s\\in S\\}$ is dense in $L^p(G,\\omega)$. In this paper, we characterize the existence of $(\\Gamma,S)$-dense vectors in $L^p(G,\\omega)$ in terms of the weight and the set $\\Gamma$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-22T15:07:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A16",
      "43A15",
      "37C85"
    ],
    "keywords": [
      "locally compact group",
      "translates",
      "supercyclicity",
      "left translation operator",
      "weight function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}