Models for the Speiser class
Models for the Speiser class
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Speiser级型号
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发表时间：
2017
期刊：
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通讯作者：
C. Bishop
中科院分区：
文献类型：
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作者：
C. Bishop
Eremenko-Lyubich类B由具有有界奇异集的超越整函数组成，Speiser类S ∈ B由具有有限奇异集的函数组成.在早期的工作（J.隆德。Math.Soc.92（2015）202-221），我给出了一种构造Eremenko-Lyubich函数的方法，该函数近似于某些称为模型的更简单的函数。在本文中，我表明，所有的模型可以近似在一个较弱的意义上的Speiser类功能，并更强的近似早期的工作（J.隆德。Math.Soc.92（2015）202-221）对于Speiser类可能失败。特别是，我给几何限制的几何的Speiser类函数，不需要满足一般Eremenko-Lyubich功能。
The Eremenko–Lyubich class B consists of transcendental entire functions with bounded singular set and the Speiser class S⊂B is made up of functions with a finite singular set. In an earlier work (J. Lond. Math. Soc. 92 (2015) 202–221), I gave a method for constructing Eremenko–Lyubich functions that approximate certain simpler functions called models. In this paper, I show that all models can be approximated in a weaker sense by Speiser class functions, and that the stronger approximation of the earlier work (J. Lond. Math. Soc. 92 (2015) 202–221) 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.