Models for the Speiser class
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912176432742400 |
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| author | Bishop, Christopher J. |
| author_facet | Bishop, Christopher J. |
| contents | The Eremenko-Lyubich class consists of transcendental entire functions with bounded singular set and the Speiser class is made up of functions with a finite singular set. In an earlier paper "Models for the Eremenko-Lyubich class" I gave a method for constructing Eremenko-Lyubich functions that approximate certain simpler functions called models. In this paper, I show that all such models can be approximated in a weaker sense by Speiser class functions, and that the stronger approximation possible using Eemenko-Lyubich functions can fail for the Speiser class. In particular, I give geometric restrictions on the geometry of a Speiser class function that need not be satisfied by general Eremenko-Lyubich functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01931 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Models for the Speiser class Bishop, Christopher J. Complex Variables 30D15 (30C62 37F10) The Eremenko-Lyubich class consists of transcendental entire functions with bounded singular set and the Speiser class is made up of functions with a finite singular set. In an earlier paper "Models for the Eremenko-Lyubich class" I gave a method for constructing Eremenko-Lyubich functions that approximate certain simpler functions called models. In this paper, I show that all such models can be approximated in a weaker sense by Speiser class functions, and that the stronger approximation possible using Eemenko-Lyubich functions can fail for the Speiser class. In particular, I give geometric restrictions on the geometry of a Speiser class function that need not be satisfied by general Eremenko-Lyubich functions. |
| title | Models for the Speiser class |
| topic | Complex Variables 30D15 (30C62 37F10) |
| url | https://arxiv.org/abs/2501.01931 |