Rate of growth of random analytic functions, with an application to linear dynamics
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914940429795328 |
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| author | Agneessens, Kevin Grosse-Erdmann, Karl-G. |
| author_facet | Agneessens, Kevin Grosse-Erdmann, Karl-G. |
| contents | We obtain Wiman-Valiron type inequalities for random entire functions and for random analytic functions on the unit disk that improve a classical result of Erdős and Rényi and recent results of Kuryliak and Skaskiv. Our results are then applied to linear dynamics: we obtain rates of growth, outside some exceptional set, for analytic functions that are frequently hypercyclic for an arbitrary chaotic weighted backward shift. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04235 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rate of growth of random analytic functions, with an application to linear dynamics Agneessens, Kevin Grosse-Erdmann, Karl-G. Complex Variables Functional Analysis 30B20, 30D20, 47A16 We obtain Wiman-Valiron type inequalities for random entire functions and for random analytic functions on the unit disk that improve a classical result of Erdős and Rényi and recent results of Kuryliak and Skaskiv. Our results are then applied to linear dynamics: we obtain rates of growth, outside some exceptional set, for analytic functions that are frequently hypercyclic for an arbitrary chaotic weighted backward shift. |
| title | Rate of growth of random analytic functions, with an application to linear dynamics |
| topic | Complex Variables Functional Analysis 30B20, 30D20, 47A16 |
| url | https://arxiv.org/abs/2409.04235 |