Chebyshev Polynomials on Compact Sets

被引：0
作者：
Vilmos Totik
机构：
[1] University of Szeged,Bolyai Institute, Analysis Research Group of the Hungarian Academy os Sciences
[2] University of South Florida,Department of Mathematics and Statistics
来源：
Potential Analysis | 2014年 / 40卷
关键词：
Chebyshev polynomials; Compact sets; Minimal norm; 31A15; 41A10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In connection with a problem of H. Widom it is shown that if a compact set K on the complex plane contains a smooth Jordan arc on its outer boundary, then the minimal norm of monic polynomials of degree n = 1,2,... is at least (1 + β)cap(K)n with some β > 0, where cap(K)n would be the theoretical lower bound. It is also shown that the rate (1 + o(1))cap(K)n is possible only for compact for which the unbounded component of the complement is simply connected. A related result for sets lying on the real line is also proven.
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页码：511 / 524
页数：13
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