Weighted Markov-type inequalities, norms of Volterra operators, and zeros of Bessel functions

被引：14

作者：

Boettcher, Albrecht ^{[1
]}

Doerfler, Peter ^{[2
]}

机构：

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

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

来源：

MATHEMATISCHE NACHRICHTEN | 2010年 / 283卷 / 01期

关键词：

Markov-type inequality; orthogonal polynomials; Volterra integral operators; Bessel function; singular values; CAUCHY TRANSFORM; DIFFERENTIATED EXPANSIONS; HALF-LINE; POLYNOMIALS; DERIVATIVES; COEFFICIENTS; EIGENVALUES; CONSTANTS; POWERS; L-2;

D O I：

10.1002/mana.200810274

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The first term of the asymptotics of the best constants in Markov-type inequalities for higher derivatives of polynomials is determined in the two cases where the underlying norm is the L(2) norm with Laguerre weight or the L(2) norm with Gegenbauer weight. The coefficient in this term is shown to be the norm of a certain Volterra integral operator which depends on the weight and the order of the derivative. For first order derivatives, the norms of the Volterra operators are expressed in terms of the zeros of Bessel functions. The asymptotic behavior of the coefficients is studied and tight bounds for them are given. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：40 / 57

页数：18

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