Universal Taylor series have a strong form of universality

被引：0

作者：

Frédéric Bayart

Vassili Nestoridis

机构：

[1] Université Bordeaux 1,Laboratoire Bordelais d’Analyse et de Géométrie, UMR 5467

[2] University of Athens,Department of Mathematics, Panepistimiopilis

来源：

Journal d'Analyse Mathématique | 2008年 / 104卷

关键词：

Natural Number; Compact Subset; Holomorphic Function; Taylor Series; Uniform Convergence;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We prove that a function f holomorphic in a simply connected domain Ω whose Taylor series at ξ ∈ Ω is universal with respect to overconvergence automatically has a strong kind of universality: its expansion in Faber series corresponding to any connected compact set Γ ⊂ Ω with [graphic not available: see fulltext] connected is universal, and we may take a supremum over all such Γ’s in a compact set. The topology used here is the Carathéodory topology. This answers a question of Mayenberger and Müller.

引用

页码：69 / 82

页数：13

共 13 条

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[9]

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[10]

Vlachou V.(undefined)undefined undefined undefined undefined-undefined

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