给定极点的有理函数插值序列的收敛性

On Convergence of the Interpolation Sequence of Rational Functions with Preassigned Poles

中文关键词:  广义Faber-Dzrbasjan有理函数系  Lagrange插值有理函数  一致逼近  平均逼近．

英文关键词:generalized Faber-Dzrbasjan rational functions  Lagrange interpolation rational functions  uniform approximation  mean approximation.

中文摘要:

      设Γ∈Ｃ（１，α），α＞０．Ｇ是复平面上以Γ为边界的有界单连通区域．本文考虑了极点位于G外部，以广义Ｆａｂｅｒ-Ｄzｒｂａsｊａｎ有理函数的零点为插值结点的Ｌａｇｒａｎｇｅ插值有理函数序列对Ａ（G）和Ｅ^ｑ（Ｇ）（１＜ｑ＜＋∞）中函数的一致逼近和平均逼近阶的估计．

英文摘要:

      Let G be a bounded simply connected domain in the complex plan with boundary ?G=Γ∈C(1,α),0<α<1 . In this paper we estimate the uniform and mean approximation orders of functions in A(G) and Ｅ^ｑ（Ｇ）（１＜ｑ＜＋∞）by their Lagrange in terpolation rational functions based on the zeros of the generalized Faber-Dzerbasejan rational functions with preassigned poles in the exterior of G.