The distribution of zeros and poles of asymptotically extremal rational functions for Zolotarev's problem

被引：1

作者：

Levin, AL

Saff, EB

机构：

[1] Open Univ Israel, Dept Math, Tel Aviv, Israel

[2] Univ S Florida, Dept Math, Inst Construct Math, Tampa, FL 33620 USA

来源：

JOURNAL OF APPROXIMATION THEORY | 2001年 / 110卷 / 01期

基金：

美国国家科学基金会;

关键词：

Zolotarev problem; rational functions; asymptotic distributions; zeros and poles; potential theory;

D O I：

10.1006/jath.2000.3551

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the possible limit distributions of zeros and poles associated with ray sequences of rational functions that are asymptotically optimal for weighted Zolotarev problems. For disjoint compacta E-1, E-2 in the complex plane, the Zolotarev problem entails minimizing the ratio of the sup over E-1 of the modulus of a weighted rational to its inf over E-2. Potential theoretic tools are utilized in the analysis. (C) 2001 Academic Press.

引用

页码：88 / 108

页数：21

共 6 条

[1] The asymptotic distribution of zeros of minimal Blaschke products [J].