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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | https://arxiv.org/abs/2601.08651 |
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| _version_ | 1866915787905695744 |
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| author | Ziarati, Pouriya Torkinejad |
| author_facet | Ziarati, Pouriya Torkinejad |
| contents | 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 $α_c \in [\frac12,2]$ such that the function is cyclic in $D_α(\B_2)$ if and only if $α\leq α_c$. To this end, we use the notion of \emph{interpolation sets} in smooth ball algebras, as studied by Bruna, Ortega, Chaumat, and Chollet. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08651 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Examples of critically cyclic functions in the Dirichlet spaces of the ball Ziarati, Pouriya Torkinejad Complex Variables Functional Analysis 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 $α_c \in [\frac12,2]$ such that the function is cyclic in $D_α(\B_2)$ if and only if $α\leq α_c$. To this end, we use the notion of \emph{interpolation sets} in smooth ball algebras, as studied by Bruna, Ortega, Chaumat, and Chollet. |
| title | Examples of critically cyclic functions in the Dirichlet spaces of the ball |
| topic | Complex Variables Functional Analysis |
| url | https://arxiv.org/abs/2601.08651 |