一类逼近算子的逼近度与保解析性

Degree of Approximation and Analytic-preserving Property of A Class of Approximation Operators

研究了一类新的有理逼近算子Ｐ＿Ｎ的逼近度与保解析（ａｎａｌｙｔｉｃ－ｐｒｅ－ｓｅｒｖｉｎｇ）特性，推导了逼近误差的估计式｜Ｒ＿Ｎｈ（ｚ）｜≤Ｃ＿ｊｈ￣（２ｊ＋１）｜ｚ｜＜ｒ，ｒ≤Ｒ并给出了“若ｈ（ｚ）在｜ｚ｜＜ｒ上解折，则Ｐ＿Ｎｈ（ｚ）亦然”，以及Ｐ＿Ｎｈ（ｚ）的递推关系等结果。

The authors deal with a class of rational approximation operators P_N and their degree of approximation and analytic-preserving property,derive the expression of the form |R_Nh(z)|≤C_jh￣(2j+1) |z|<r,r≤R for the error in approximation of the operator,and give the results on the analyticity of P_Nh(z),the recurrence relation for P_Nh(z),etc.