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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2503.23987 |
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| _version_ | 1866915219240910848 |
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| author | Bergqvist, Linus Limani, Adem Malman, Bartosz |
| author_facet | Bergqvist, Linus Limani, Adem Malman, Bartosz |
| contents | We revisit the problem of characterizing cyclic elements for the shift operator in a broad class of radial growth spaces of holomorphic functions on the unit disk, focusing on functions of finite Nevanlinna characteristic. We provide results in the range of Dini regular weights, and in the regime of logarithmic integral divergence. Our proofs are largely constructive, enabling us to simplify and extend a classical result by Korenblum and Roberts, and a recent Theorem due to El-Fallah, Kellay, and Seip. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23987 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Revisiting cyclic elements in growth spaces Bergqvist, Linus Limani, Adem Malman, Bartosz Complex Variables Functional Analysis 30J15, 30H20, 30H15 We revisit the problem of characterizing cyclic elements for the shift operator in a broad class of radial growth spaces of holomorphic functions on the unit disk, focusing on functions of finite Nevanlinna characteristic. We provide results in the range of Dini regular weights, and in the regime of logarithmic integral divergence. Our proofs are largely constructive, enabling us to simplify and extend a classical result by Korenblum and Roberts, and a recent Theorem due to El-Fallah, Kellay, and Seip. |
| title | Revisiting cyclic elements in growth spaces |
| topic | Complex Variables Functional Analysis 30J15, 30H20, 30H15 |
| url | https://arxiv.org/abs/2503.23987 |