论布洛赫的 "拓扑连续性原理"

Pub Date : 2024-04-04 DOI:10.1007/s40315-024-00531-w

Walter Bergweiler, Alexandre Eremenko

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引用次数: 0

摘要

我们讨论了如果只假定某个约旦域上的所有岛都是多重的，从而放宽某些值是完全夯实的这一假设，那么关于全函数和分形函数的完全夯实值的某些结果在多大程度上仍然有效。特别是，我们证明了布洛赫提出的一个结果，即一个阶小于 1 的全函数在两个给定的约旦域中至少有一个具有不相交的闭合域上有一个简单岛。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On Bloch’s “Principle of Topological Continuity”

We discuss to what extent certain results about totally ramified values of entire and meromorphic functions remain valid if one relaxes the hypothesis that some value is totally ramified by assuming only that all islands over some Jordan domain are multiple. In particular, we prove a result suggested by Bloch which says that an entire function of order less than 1 has a simple island over at least one of two given Jordan domains with disjoint closures.

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