一类新的Lagrange型三角插值多项式及其在Lp空间中的收敛性

A New KIND OF LAGRANGE TYPE TRIGONOMETRIC INTERPOLATIONPOLYNOMIALS AND ITS CONVERGENCE IN L P SPACES

本文引进了一类以ｘｋ＝２ｋπ２ｎ＋１（ｋ＝０，１，…，２ｎ）为插值结点的新的Ｌａｇｒａｎｇｅ型三角插值多项式，并讨论了该插值多项式在ＬＰ空间中的逼近性质。

In this paper we introduce a new kind of Lagrange type trigonometric interpolation polynomials with the nodes x k=2kπ2n+1(k=0,1, ,2n) and consider the convergence of these operators in L P spaces.