Tractability of sampling recovery on unweighted function classes

04/27/2023

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by   David Krieg, et al.

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It is well-known that the problem of sampling recovery in the L_2-norm on unweighted Korobov spaces (Sobolev spaces with mixed smoothness) as well as classical smoothness classes such as Hölder classes suffers from the curse of dimensionality. We show that the problem is tractable for those classes if they are intersected with the Wiener algebra of functions with summable Fourier coefficients. In fact, this is a relatively simple implication of powerful results by Rauhut and Ward [Appl. Comput. Harmon. Anal. 40 (2016), pp. 321–351]. Tractability is achieved by the use of non-linear algorithms, while linear algorithms cannot do the job.