On Beurling’s boundary differential relation

被引：0
|
作者：
Miran Černe
Manuel Flores
机构：
[1] University of Ljubljana,Department of Mathematics
[2] University of La Laguna,Department of Mathematics
来源：
Israel Journal of Mathematics | 2014年 / 199卷
关键词：
Univalent Solution; Holomorphic Function; Free Boundary; Univalent Function; Riemann Mapping;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We prove that for an arbitrary positive continuous function Φ on the complex plane ℂ there exists an injective disc algebra function φ and n ∈ ℕ such that ξ ↦ φ(ξn) solves Beurling’s boundary differential relation |f′(ξ)| = Φ(f(ξ)) on ∂Δ. Moreover, if the growth of Φ is sublinear, the existence of univalent solutions of Beurling’s boundary differential relation is shown.
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页码：831 / 840
页数：9
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