Universal Taylor Series in Simply Connected Domains

被引：0

作者：

Christos Kariofillis

Vassili Nestoridis

机构：

[1] Aristotel University of Thessaloniki,Department of Mathematics, Faculty of Sciences

[2] University of Athens,Department of Mathematics

来源：

Computational Methods and Function Theory | 2006年 / 6卷 / 2期

关键词：

Generic property; overconvergence; Taylor series; natural boundary; universal functions; 30B30-41;

D O I：

10.1007/BF03321621

中图分类号：

学科分类号：

摘要：

Let Ω be a simply connected domain in ℂ For a function f holomorphic in Ω let Sn (f, ζ) denote the partial sum of the Taylor development of f with center ζ ∈ Ω. We show that generically overconvergence phenomena of Sn(f, ζ) and their derivatives can occur on the boundary ∂Ω or in parts of it. In the rest of the boundary ∂Ω, the universal function f may be smooth. These parts of the boundary do not have to be connected.

引用

页码：437 / 446

页数：9

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