论文标题
kolmogorov宽度的界限和较小混合平滑度的类的采样恢复
Bounds on Kolmogorov widths and sampling recovery for classes with small mixed smoothness
论文作者
论文摘要
在论文中获得了具有混合平滑度的功能类别的渐近特征的结果。我们的主要兴趣是估计具有较小混合平滑度的类的Kolmogorov宽度。我们证明了三角多项式的单位球具有来自双曲线交叉的频率的相应边界。我们演示了我们在Kolmogorov宽度上的结果如何意味着新的上限，以在$ l_2 $的功能范围内进行最佳采样恢复，并具有较小的混合光滑度。
Results on asymptotic characteristics of classes of functions with mixed smoothness are obtained in the paper. Our main interest is in estimating the Kolmogorov widths of classes with small mixed smoothness. We prove the corresponding bounds for the unit balls of the trigonometric polynomials with frequencies from a hyperbolic cross. We demonstrate how our results on the Kolmogorov widths imply new upper bounds for the optimal sampling recovery in the $L_2$ norm of functions with small mixed smoothness.
