UNIVERSAL TAYLOR SERIES, CONFORMAL MAPPINGS AND BOUNDARY BEHAVIOUR

被引：10

作者：

Gardiner, Stephen J. ^{[1
]}

机构：

[1] Univ Coll Dublin, Sch Math Sci, Dublin 4, Ireland

来源：

ANNALES DE L INSTITUT FOURIER | 2014年 / 64卷 / 01期

关键词：

Universal Taylor series; conformal mappings; angular boundary behaviour;

D O I：

10.5802/aif.2849

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A holomorphic function f on a simply connected domain 12 is said to possess a universal Taylor series about a point in Omega if the partial sums of that series approximate arbitrary polynomials on arbitrary compacta K outside 52 (provided only that K has connected complement). This paper shows that this property is not conformally invariant, and, in the case where Cl is the unit disc, that such functions have extreme angular boundary behaviour.

引用

页码：327 / 339

页数：13

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