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.
引用
收藏
页码：511 / 524
页数：13
相关论文
共 50 条
[31]   Embedding Distributions and Chebyshev Polynomials [J].
Chen, Yichao ;
Mansour, Toufik ;
Zou, Qian .
GRAPHS AND COMBINATORICS, 2012, 28 (05) :597-614
[32]   Chebyshev polynomials on circular arcs [J].
Schiefermayr, Klaus .
ACTA SCIENTIARUM MATHEMATICARUM, 2019, 85 (3-5) :629-649
[33]   Optimization via Chebyshev polynomials [J].
Elgindy, Kareem T. .
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2018, 56 (1-2) :317-349
[34]   An alternative formula for Chebyshev polynomials [J].
Nadarajah, Saralees .
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2008, 19 (06) :409-411
[35]   Decomposition of perturbed Chebyshev polynomials [J].
Stoll, Thomas .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 214 (02) :356-370
[36]   Some properties of Chebyshev polynomials [J].
Kim, Seon-Hong .
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2012,
[37]   Combinatorial trigonometry with Chebyshev polynomials [J].
Benjamin, Arthur T. ;
Ericksen, Larry ;
Jayawant, Pallavi ;
Shattuck, Mark .
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2010, 140 (08) :2157-2160
[38]   A characterization of the Chebyshev and Fibonacci polynomials [J].
Cuccoli M. ;
Ricci P.E. .
Rendiconti del Circolo Matematico di Palermo, 1998, 47 (1) :129-140
[39]   Discrete Entropies of Chebyshev Polynomials [J].
Sfetcu, Razvan-Cornel ;
Sfetcu, Sorina-Cezarina ;
Preda, Vasile .
MATHEMATICS, 2024, 12 (07)
[40]   Optimization via Chebyshev polynomials [J].
Kareem T. Elgindy .
Journal of Applied Mathematics and Computing, 2018, 56 :317-349
12345