修正高阶Hermite插值及Hermite-Fejer插值在L_ω～p空间中逼近的正逆定理(英文)

The Inverse Theorems for Modified Higher Order Hermite Interpolation and Hermite-Fejér Interpolation in L_w^p Spaces

在L_ω～p空间中引入了一种 K-泛函并由此建立了一种以第一类 Chebyshev多项式的零点为结点的三种修正高阶 Hermite-Fejer插值多项式及一种修正的高阶 Hermite插值多项式在L_ω～p空间中逼近的正逆定理. 文中的结果说明,对于这几种修正高阶多项式插值的逼近问题而言,正定理的解决意味着逆定理的解决.

A kind of K-functional in l?, is proposed, with which the direct and inverse theorems of approximation by three kinds of modified higher order Hermite-Fejer interpolations and a kind of modified higher order Hermite interpolation on Chebyshev nodes are established. The results obtained in this paper actually imply that the establishment of the direct theorem will result in the establishment of the inverse theorem for the modified higher Hermite-Fejer interpolation and the modified higher Hermite interpolation.