{
  "annotation_id": "7f63d65b-0ff2-4775-8caf-28918c2564b1",
  "date_created": "2026-02-17T05:53:16.248000Z",
  "date_modified": "2026-02-17T05:53:16.248000Z",
  "file_hash": "6ba51801221b92c155d6bb983727c15f8625121a6c3ce60ea4c01b23140232b1",
  "private": false,
  "record": {
    "abstract": "In this work, we construct examples of holomorphic functions in $D_2(\\B_2)$, the Dirichlet space on $\\B_2$, for which there exists an index $\\alpha_c \\in [\\frac12,2]$ such that the function is cyclic in $D_\\alpha(\\B_2)$ if and only if $\\alpha \\leq \\alpha_c$. To this end, we use the notion of \\emph{interpolation sets} in smooth ball algebras, as studied by Bruna, Ortega, Chaumat, and Chollet.",
    "arxiv_id": "2601.08651",
    "authors": [
      "Pouriya Torkinejad Ziarati"
    ],
    "categories": [
      "math.CV",
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Examples of critically cyclic functions in the Dirichlet spaces of the ball",
    "url": "https://arxiv.org/abs/2601.08651",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "60ac664c-e669-4c72-b610-1f2a3b36d901",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}