Bounds on Kolmogorov widths and sampling recovery for classes with small mixed smoothness

Temlyakov V; Ullrich T.

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Bounds on Kolmogorov widths and sampling recovery for classes with small mixed smoothness

机译：Bounds on Kolmogorov widths and sampling recovery for classes with small mixed smoothness

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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 in the uniform norm 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. (C) 2021 Elsevier Inc. All rights reserved.

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《Journal of complexity》 |2021年第12期|101575.1-101575.19|共19页
作者
Temlyakov V; Ullrich T.;
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Univ South Carolina, Columbia, SC 29208 USA|Steklov Inst Math, Moscow, Russia|Lomonosov Moscow State Univ, Moscow, Russia|Moscow Ctr Fundamental & Appl Math, Moscow, Russia;

Fac Math, D-09107 Chemnitz, Germany;

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正文语种英语
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Kolmogorov width; Recovery; Small smoothness;

Bounds on Kolmogorov widths and sampling recovery for classes with small mixed smoothness

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