{
  "id": "1703.06775",
  "version": "v1",
  "published": "2017-03-20T14:38:59.000Z",
  "updated": "2017-03-20T14:38:59.000Z",
  "title": "Density of translates in weighted $L^p$ spaces on locally compact groups",
  "authors": [
    "Evgeny Abakumov",
    "Yulia Kuznetsova"
  ],
  "comment": "to appear in Monatshefte f\\\"ur Mathematik",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $G$ be a locally compact group, and let $1\\le p < \\infty$. Consider the weighted $L^p$-space $L^p(G,\\omega)=\\{f:\\int|f\\omega|^p<\\infty\\}$, where $\\omega:G\\to \\mathbb R$ is a positive measurable function. Under appropriate conditions on $\\omega$, $G$ acts on $L^p(G,\\omega)$ by translations. When is this action hypercyclic, that is, there is a function in this space such that the set of all its translations is dense in $L^p(G,\\omega)$? H. Salas (1995) gave a criterion of hypercyclicity in the case $G=\\mathbb Z$ . Under mild assumptions, we present a corresponding characterization for a general locally compact group $G$. Our results are obtained in a more general setting when the translations only by a subset $S\\subset G$ are considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-20T14:38:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A16",
      "37C85",
      "43A15"
    ],
    "keywords": [
      "translates",
      "general locally compact group",
      "translations",
      "action hypercyclic",
      "mild assumptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}