比伯巴赫多项式的收敛性:Keldysh定理和Mergelyan猜想

IF 1.4 4区数学 Q1 MATHEMATICS

Russian Mathematical Surveys Pub Date : 2021-01-01 DOI:10.1070/RM9991

A. Aptekarev

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引用次数: 0

摘要

考虑了Keldysh关于比伯巴赫多项式的收敛性和解析函数空间中多项式的密度的结果。讨论了它们在建设性复杂分析的当代背景下的进一步发展和相关性。重点讨论了Mergelyan关于光滑边界域的收敛速度的猜想，该猜想仍然是开放的。参考书目:20篇。

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Convergence of Bieberbach polynomials: Keldysh’s theorems and Mergelyan’s conjecture

Results due to Keldysh on the convergence of Bieberbach polynomials and the density of polynomials in spaces of analytic functions are considered. Their further development and relevance in the contemporary context of constructive complex analysis are discussed. Particular focus is placed on Mergelyan’s conjecture on the rate of convergence in a domain with smooth boundary, which is still open. Bibliography: 20 titles.

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来源期刊

Russian Mathematical Surveys 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Mathematical Surveys is a high-prestige journal covering a wide area of mathematics. The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The survey articles on current trends in mathematics are generally written by leading experts in the field at the request of the Editorial Board.