论文标题
对高光滑度周期函数卷积类别的最佳均匀近似值的渐近估计值
Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothness
论文作者
论文摘要
我们发现，从空间单位球$ l_p的单位球，1 \ le p <\ infty，带固定核的$ l_p，$ 2 $ 2 $的卷积的最佳均匀近似值的两面估计值$ \ sum \ limits_ {k = n+1}^\inftyψ（k）= o（1）ψ（n）$所获得的估计值成为渐近相等性。
We find two-sides estimates for the best uniform approximations of classes of convolutions of $2π$-periodic functions from unit ball of the space $L_p, 1 \le p <\infty,$ with fixed kernels, modules of Fourier coefficients of which satisfy the condition $\sum\limits_{k=n+1}^\inftyψ(k)<ψ(n).$ In the case of $\sum\limits_{k=n+1}^\inftyψ(k)=o(1)ψ(n)$ the obtained estimates become the asymptotic equalities.
