On the Hölder semi-norm of the remainder in polynomial approximation
On the Hölder semi-norm of the remainder in polynomial approximation
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关于多项式逼近中余数的Hölder半范数
DOI：
10.1017/s000497270001652x
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发表时间：
1994
影响因子：
0.7
通讯作者：
D. Elliott
中科院分区：
文献类型：
--
作者：
D. Elliott
Suppose the qth derivative of a function f is Hölder continuous of index α, where 0 < α ≤ 1, on the interval [-1,1]. Suppose further that pn is any polynomial of degree at most n such that |τn(x)| = |f(x) - pn(x)| ≤ c {max ((1 - x2)½/n, 1/n2) } q+a [-1,1]. If then it is shown that ‖τn‖β ≤ cn−q−α+β, 0 < β ≤ 1.
