用具有对数奇点的函数类逼近闭曲线上的连续函数

APPROXIMATION OF CONTINUOUS FUNCTIONS ON CLOSED CURVE BY A CLASS OF FUNCTIONS WITH LOGARITHMIC SINGULARITIES

讨论用函数类Ａｎ（ｚ）λ（ｚ）＋Ｂｎ（ｚ）均匀逼近闭曲线上的连续函数的问题，其中Ａｎ（ｚ），Ｂｎ（ｚ）是不大于ｎ次的多项式，λ（ｚ）＝ｌｏｇｚ＋ａｚ＋ｂ或（ｚ＋ａｚ＋ｂ）α（０＜α＜１）．

It is discussed that the question of uniform approximation of continuous functions on a closed curve by A n(z)λ(z)+B n(z) ,where A n(z),B n(z) are polynomials, λ(z)= log z+az+b or (z+az+b) α(0<α<1); The corresponding Weierstrass type and Jackson type theorems for a kind of closed curve are given.