On optimal recovery in L_2

10/07/2020

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by   V. Temlyakov, et al.

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We prove that the optimal error of recovery in the L_2 norm of functions from a class can be bounded above by the value of the Kolmogorov width of in the uniform norm. We demonstrate on a number of examples of from classes of functions with mixed smoothness that the obtained inequality provides a powerful tool for estimating errors of optimal recovery.