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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2508.05189 |
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| _version_ | 1866912933377736704 |
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| author | Ziarati, Pouriya Torkinejad |
| author_facet | Ziarati, Pouriya Torkinejad |
| contents | We study the cyclicity of multipliers in Dirichlet-type spaces \( D_α(\mathbb{B}_n) \). Specifically, we show that a multiplier \( f \) analytic on a neighborhood of $\overline{\mathbb{B}}_n$, whose zero set on the unit sphere is a compact, smooth, complex tangential submanifold of real dimension \( m \leq n - 1 \), is cyclic in \( D_α(\mathbb{B}_n) \) if and only if \( α\leq \frac{2n - m}{2} \). Our approach combines classical results on peak sets in \( A^\infty(\mathbb{B}_n) \) due to Chaumat and Chollet with a Corona-type theorem with two generators for the multiplier algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05189 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cyclicity of Multipliers on the Unit Ball of $\mathbb{C}^n$: A Corona-Based Approach Ziarati, Pouriya Torkinejad Complex Variables Functional Analysis We study the cyclicity of multipliers in Dirichlet-type spaces \( D_α(\mathbb{B}_n) \). Specifically, we show that a multiplier \( f \) analytic on a neighborhood of $\overline{\mathbb{B}}_n$, whose zero set on the unit sphere is a compact, smooth, complex tangential submanifold of real dimension \( m \leq n - 1 \), is cyclic in \( D_α(\mathbb{B}_n) \) if and only if \( α\leq \frac{2n - m}{2} \). Our approach combines classical results on peak sets in \( A^\infty(\mathbb{B}_n) \) due to Chaumat and Chollet with a Corona-type theorem with two generators for the multiplier algebra. |
| title | Cyclicity of Multipliers on the Unit Ball of $\mathbb{C}^n$: A Corona-Based Approach |
| topic | Complex Variables Functional Analysis |
| url | https://arxiv.org/abs/2508.05189 |