插值理论的一个引理及其应用

A Lemma in Interpolation Theory and It's Applications

本文指出了Erdos,Kroó和Szabados的一个重要引理的证明中出现的错误,并纠正其错误,还给出了此引理的两个应用,其中之一指出当第一类Chebyshev结点产生很小的扰动时,相应的Hermite—Fejér插值仍能保证对任意连续函数的一致逼近性,从而拓广了Fejér及Saxena的经典结论。

In this paper ,some mistakes in the proof of a important lemma of Erdos ,kroo andSzabados are pointed out,and a correct proof is given. We give out also two applications of this lemma,one of which shows that when the distrubence is quite small,the Hermite - Fejer interpolation polynomial based on the disturbed Chebyshev nodes of the first kind may convergent uniformly for all continuous functions. This extends the classical results of Fejer and Saxena.