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 50 条

[21] DISTRIBUTION OF ZEROS AND POLES OF MEROMORPHIC FUNCTIONS AND THEIR FILLING DISKS
YANG, L
ZHANG, GH
SCIENTIA SINICA SERIES A-MATHEMATICAL PHYSICAL ASTRONOMICAL & TECHNICAL SCIENCES, 1982, 25 (04): : 371 - 383
[22] Universality and distribution of zeros and poles of some zeta functions
Kristian Seip
Journal d'Analyse Mathématique, 2020, 141 : 331 - 381
[23] Generalizations of some inequalities for rational functions with prescribed poles and restricted zeros
Preeti Gupta
Sunil Hans
Abdullah Mir
Analysis and Mathematical Physics, 2022, 12
[24] Generalizations of some inequalities for rational functions with prescribed poles and restricted zeros
Gupta, Preeti
Hans, Sunil
Mir, Abdullah
ANALYSIS AND MATHEMATICAL PHYSICS, 2022, 12 (01)
[25] Extremal Rational Functions on Several Arcs of the Unit Circle with Zeros on these Arcs
Lukashov, A. L.
Tyshkevich, S. V.
IZVESTIYA SARATOVSKOGO UNIVERSITETA NOVAYA SERIYA-MATEMATIKA MEKHANIKA INFORMATIKA, 2009, 9 (01): : 8 - 13
[26] Distribution of Zeros for Random Laurent Rational Functions
Igor E. Pritsker
Computational Methods and Function Theory, 2018, 18 : 143 - 157
[27] Distribution of Zeros for Random Laurent Rational Functions
Pritsker, Igor E.
COMPUTATIONAL METHODS AND FUNCTION THEORY, 2018, 18 (01) : 143 - 157
[28] DISTRIBUTION OF POLES OF DIAGONAL RATIONAL APPROXIMANTS TO FUNCTIONS OF FAST RATIONAL APPROXIMABILITY
LUBINSKY, DS
CONSTRUCTIVE APPROXIMATION, 1991, 7 (04) : 501 - 519
[29] ON THE ZEROS OF RATIONAL FUNCTIONS HAVING PRESCRIBED POLES, WITH APPLICATIONS TO THE DERIVATIVE OF AN ENTIRE FUNCTION OF FINITE GENRE
MARDEN, M
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1949, 66 (JUL-) : 407 - 418
[30] Extremal Problems of Turan-type Involving the Location of All Zeros of a Class of Rational Functions
Mir, M. Y.
Wali, S. L.
Shah, W. M.
VESTNIK ST PETERSBURG UNIVERSITY-MATHEMATICS, 2024, 57 (02) : 219 - 225

← 1 2 3 4 5 →