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

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外部，以广义ＦａｂｅｒＤｒｂａｊａｎ有理函数的零点为插值结点的Ｌａｇｒａｎｇｅ插值有理函数序列对Ａ（）和Ｅｑ（Ｇ）（１＜ｑ＜＋∞）中函数的一致逼近和平均逼近阶的估计．

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() and E q(G)(1<q<+∞) by their Lagrange interpolation rational functions based on the zeros of the generalized Faber Drbajan rational functions with preassigned poles in the exterior of .