Derivatives of Faber polynomials and Markov inequalities

被引：3

作者：

Pritsker, IE ^{[1
]}

机构：

[1] Oklahoma State Univ, Dept Math, Stillwater, OK 74078 USA

来源：

JOURNAL OF APPROXIMATION THEORY | 2002年 / 118卷 / 02期

基金：

美国国家科学基金会;

关键词：

Asymptotics; Derivatives; Faber polynomials; Markov inequalities;

D O I：

10.1006/jath.2002.3713

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study asymptotic behavior of the derivatives of Faber polynomials on a set with corners at the boundary. Our results have applications to the questions of sharpness of Markov inequalities for such sets. In particular, the found asymptotics are related to a general Markov-type inequality of Pommerenke and the associated conjecture of Erdos. We also prove a new bound for Faber polynomials on piecewise smooth domains. (C) 2002 Elsevier Science (USA).

引用

页码：163 / 174

页数：12

共 50 条

[21] Zeros of Faber Polynomials for Joukowski Airfoils [J].

Levenberg, N. ;

Wielonsky, F. .

CONSTRUCTIVE APPROXIMATION, 2020, 52 (01) :93-114

[22] Zeros of Faber Polynomials for Joukowski Airfoils [J].

N. Levenberg ;

F. Wielonsky .

Constructive Approximation, 2020, 52 :93-114

[23] Faber Polynomials on Quaternionic Compact Sets [J].

Gal, Sorin G. ;

Sabadini, Irene .

COMPLEX ANALYSIS AND OPERATOR THEORY, 2017, 11 (05) :1205-1220

[24] EXPLICIT FABER POLYNOMIALS ON CIRCULAR SECTORS [J].

GATERMANN, K ;

HOFFMANN, C ;

OPFER, G .

MATHEMATICS OF COMPUTATION, 1992, 58 (197) :241-&

[25] On the best constants in inequalities of the Markov and Wirtinger types for polynomials on the half-line [J].

Boettcher, Albrecht ;

Doerfler, Peter .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (04) :1057-1069

[26] ON FABER POLYNOMIALS GENERATED BY AN M-STAR [J].

BARTOLOMEO, J ;

HE, M .

MATHEMATICS OF COMPUTATION, 1994, 62 (205) :277-287

[27] Power matrices for Faber polynomials and conformal welding [J].

Penfound, Bryan ;

Schippers, Eric .

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2013, 58 (09) :1247-1259

[28] BERNSTEIN-MARKOV TYPE INEQUALITIES AND OTHER INTERESTING ESTIMATES FOR POLYNOMIALS ON CIRCLE SECTORS [J].

Jimenez-Rodriguez, P. ;

Munoz-Fernandez, G. A. ;

Pellegrino, D. ;

Seoane-Sepulveda, J. B. .

MATHEMATICAL INEQUALITIES & APPLICATIONS, 2017, 20 (01) :285-300

[29] Bernstein-Nikolskii-Markov-type inequalities for algebraic polynomials in a weighted Lebesgue space [J].

Ozkartepe, P. ;

Imashkyzy, M. ;

Abdullayev, F. G. .

FILOMAT, 2023, 37 (17) :5701-5715

[30] THE FABER POLYNOMIALS FOR M-FOLD SYMMETRICAL DOMAINS [J].

HE, M .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1994, 54 (03) :313-324

← 1 2 3 4 5 →