{
  "id": "2309.09601",
  "version": "v1",
  "published": "2023-09-18T09:16:18.000Z",
  "updated": "2023-09-18T09:16:18.000Z",
  "title": "On cyclicity in de Branges-Rovnyak spaces",
  "authors": [
    "Alex Bergman"
  ],
  "comment": "To appear in Indiana University Mathematics Journal",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "We study the problem of characterizing the cyclic vectors in de Branges-Rovnyak spaces. Based on a description of the invariant subspaces we show that the difficulty lies entirely in understanding the subspace $(aH^{2})^{\\perp}$ and give a complete function theoretic description of the cyclic vectors in the case $\\dim (aH^{2})^{\\perp} < \\infty$. Incidentally, this implies analogous results for certain generalized Dirichlet spaces $\\mathcal{D}(\\mu)$. Most of our attention is directed to the infinite case where we relate the cyclicity problem to describing the exposed points of $H^{1}$ and provide several sufficient conditions. A necessary condition based on the Aleksandrov-Clark measures of $b$ is also presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-18T09:16:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E22"
    ],
    "keywords": [
      "branges-rovnyak spaces",
      "cyclic vectors",
      "complete function theoretic description",
      "invariant subspaces",
      "necessary condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}