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| ON THE APPROXIMAMATION OF DIFFERENTIABLE FUNCTIONS BY EULER MEANS |
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Citation： |
Xie Tingfan.ON THE APPROXIMAMATION OF DIFFERENTIABLE FUNCTIONS BY EULER MEANS[J].Chinese Annals of Mathematics B,1991,12(1):80~89 |
| Page view： 819
Net amount： 719 |
Authors： |
Xie Tingfan; |
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| Abstract： |
Let $f\in C^{r}_{2Pi}$ Denote by $\xi_{n}(f,x)$ the n-th Euler mean of $f(x)$. This paper gives the asymptotic representations of the deviation $\xi_{n}(f,x)-f(x)$ and the quantity
$$\sup\underline{\in w^{r}H_{w}}\max\underline{x}|\xi_{n}(f,x)-f(x)|.$$
Additionally, some applications of these asymptotic representations are obtained |
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