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 H\"older 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.

翻译：众所周知，在无权重Korobov空间（具有混合光滑性的Sobolev空间）以及经典光滑性类（如Hölder类）中，$L_2$范数下的采样恢复问题受维度灾难影响。我们证明，若将这些函数类与傅里叶系数可和的Wiener代数相交，则问题具有可解性。实际上，这是Rauhut和Ward的强有力结论[Appl. Comput. Harmon. Anal. 40 (2016), pp. 321--351]的一个相对简单的推论。可解性通过非线性算法实现，而线性算法无法达成该目标。