Hypercyclicity of weighted shifts on weighted Bergman spaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908661008302080 |
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| author | Das, Bibhash Kumar Mundayadan, Aneesh |
| author_facet | Das, Bibhash Kumar Mundayadan, Aneesh |
| contents | We study the continuity, and dynamical properties (hypercyclicity, periodic vectors, and chaos) for a weighted backward shift $B_w$ on a weighted Bergman space $A^p_ϕ$ based on the norm estimates of coefficient functionals on $A^p_ϕ$. Here, the weight function $ϕ(z)$ is mostly radial, but our work will also involve a (non-radial) subharmonic weight. We provide a complete characterization of hypercyclic shifts $B_w$ on $A^p_ϕ$ when $ϕ$ is an (integrable) radial weight. The coefficient multipliers obtained in this paper for certain weights are new. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_16354 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hypercyclicity of weighted shifts on weighted Bergman spaces Das, Bibhash Kumar Mundayadan, Aneesh Functional Analysis Complex Variables 47A16, 46E22, 32K05, 47B32, 47B37, 37A99 We study the continuity, and dynamical properties (hypercyclicity, periodic vectors, and chaos) for a weighted backward shift $B_w$ on a weighted Bergman space $A^p_ϕ$ based on the norm estimates of coefficient functionals on $A^p_ϕ$. Here, the weight function $ϕ(z)$ is mostly radial, but our work will also involve a (non-radial) subharmonic weight. We provide a complete characterization of hypercyclic shifts $B_w$ on $A^p_ϕ$ when $ϕ$ is an (integrable) radial weight. The coefficient multipliers obtained in this paper for certain weights are new. |
| title | Hypercyclicity of weighted shifts on weighted Bergman spaces |
| topic | Functional Analysis Complex Variables 47A16, 46E22, 32K05, 47B32, 47B37, 37A99 |
| url | https://arxiv.org/abs/2503.16354 |