INVERSE BERNSTEIN INEQUALITIES AND MIN-MAX-MIN PROBLEMS ON THE UNIT CIRCLE

被引：5

作者：

Erdelyi, Tamas ^{[1
]}

Hardin, Douglas P. ^{[2
]}

Saff, Edward B. ^{[2
]}

机构：

[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[2] Vanderbilt Univ, Dept Math, Ctr Construct Approximat, Nashville, TN 37240 USA

来源：

MATHEMATIKA | 2015年 / 61卷 / 03期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1112/S0025579314000138

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a short and elementary proof of an inverse Bernstein-type inequality found by S. Khrushohev for the derivative of a polynomial having all its zeros on the unit circle. The inequality is used to show that equally-spaced points solve a mm max-mm problem for the logarithmic potential of such polynomials. Using techniques recently developed for polarization (Chebyshev-type) problems, we show that this optimality also holds for a large class of potentials, including the Riesz potentials 1/r(s) with s > 0.

引用

页码：581 / 590

页数：10

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