On the continuity of the sharp constant in the Jackson-Stechkin inequality in the space <i>L</i> <SUP>2</SUP>

作     者：Balaganskii, V. S. 

作者机构：Russian Acad Sci Inst Math & Mech Ural Branch Ekaterinburg Russia 

出 版 物：《MATHEMATICAL NOTES》 (数学札记)

年 卷 期：2013年第93卷第1-2期

页      面：12-28页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Program for Basic Research "Dynamical Systems and Control Theory" of the Presidium Ural Branch of the Russian Academy of Sciences [12-P-1-1022] Russian Foundation for Basic Research [11-01-00347] 

主　　题：approximation of a function Jackson-Stechkin inequality trigonometric polynomial the space L-2 Tietze-Urysohn theorem modulus of continuity extremal function 

摘      要：This paper deals with the continuity of the sharp constant K(T,X) with respect to the set T in the Jackson-Stechkin inequality E(f, L) = K (T, X)omega(f, T, X), where E(f,L) is the best approximation of the function f a X by elements of the subspace L aS, X, and omega is a modulus of continuity, in the case where the space L (2)(, a,) is taken for X and the subspace of functions g a L (2)(, a,), for L. In particular, it is proved that the sharp constant in the Jackson-Stechkin inequality is continuous in the case where L is the space of trigonometric polynomials of nth order and the modulus of continuity omega is the classical modulus of continuity of rth order.