渐近单位根上的 Lagrange 插值多项式的逼近阶

ORDER OF APPOXIMATION BY LAGRANGE INTERPOLATING POLYNOMIALS AT NEARLY ROOTS OF UNITY

本文考虑渐近单位根上Lagrange插值多项式在单位园周上一致逼近及平均逼近A(|z|≤1)中函数,得到了逼近阶的估计式。进一步,指出了这个拢动程度在某种程度上还是精确的。

In this paper,the order of approximation in L^p(|w|≤1) spaces,0<P<+∞, by Lagrange interpolating polynomials at nearly roots of unity of func-tions of class A(|w|≤1) is presented.Moreover,it has been shown that ifthe condintion(1.1) is not satisfied,then the convergence in L^p(|w|≤1),p>1cannot be valid.