ON THE BEST CONSTANTS IN MARKOV-TYPE INEQUALITIES INVOLVING GEGENBAUER NORMS WITH DIFFERENT WEIGHTS

被引：0

作者：

Boettcher, Albrecht ^{[1
]}

Doerfler, Peter ^{[2
]}

机构：

[1] TU Chemnitz, Fac Math, D-09107 Chemnitz, Germany

[2] Univ Leoben, Dept Math & Informat Technol, A-8700 Leoben, Austria

来源：

OPERATORS AND MATRICES | 2011年 / 5卷 / 02期

关键词：

Markov inequality; Gegenbauer weight; ultraspherical polynomials; Toeplitz matrix; Volterra operator;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper is concerned with best constants in Markov-type inequalities between the norm of a higher derivative of a polynomial and the norm of the polynomial itself. The norm of the polynomial is taken in L-2 with the Gegenbauer weight corresponding to a parameter alpha, while the derivative is measured in L-2 with the Gegenbauer weight for a parameter beta. Under the assumption that beta - alpha is an integer, we determine the first order asymptotics of the best constants as the degree of the polynomial goes to infinity.

引用

页码：261 / 272

页数：12

共 19 条

[1] Extremal problems, inequalities, and classical orthogonal polynomials [J].