(0,p(D))三角插值多项式对函数及其导数的同时逼近  

The (0,p(D)) trigonometric interpolation polynomials' simultaneous approximation of functions and their derivatives

作　　者：金玮[1] 侯象乾[1] 马泽玲[1] 

机构地区：[1]宁夏大学数学计算机学院,银川750021

出　　处：《华中师范大学学报（自然科学版）》2004年第3期276-279,283,共5页Journal of Central China Normal University：Natural Sciences

基　　金：宁夏自然科学基金资助项目(A001);宁夏大学青年科学基金资助项目(QN032102).

摘　　要：证明了(0,p(D))三角插值多项式Rn(x)的s(s=0,1,…,q)阶导数一致收敛于函数f(x)的s(s=0,1,…,q)阶导数:设f(x)∈C2π,f(x)具有q阶连续导数,且f(q)(x)∈Lipα.0<α<1,若βk=Op(in)n(n)-f(s)(n)=Olnnnq+α,(k=0,1,2,…,n-1),则R(s)nq-s+α(s=0,1,…,q).It is proved that the sth derivative of (0,p(D)) trigonometric interpolation polynomial R_n(x) converges uniformly to f^((s))(x),(s=0,1,…,q): if (f(x))∈C_(2π),(f(x)) has qth continuous derivatives, and f^((q))(x)∈Lipα(0<α<1), if β_k=Op(in)n^(q+α)(k=0,1,…,n-1), then R^((s))_n(x)-f^((s))(x)=Olnnn^(q-s+α).(s=0,1,…,q)

关 键 词：(0 P(D))插值 一致收敛 导数 

分 类 号：O174.41[理学—数学]