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Estimates for the widths of classes of periodic functions of several variables. I. (English) Zbl 1216.41021
Summary: We establish estimates sharp in order for the Kolmogorov and linear widths of the classes $$B_{pq}^{sm}(\mathbb T^k)$$ and $$L_{pq}^{sm}(\mathbb T^k)$$ of Nikol’skii-Besov, Lizorkin-Triebel types, respectively, in the space $$L_r(\mathbb T^k)$$ for a certain range of the parameters $$s,p,q,r$$, and $$m$$.

##### MSC:
 41A46 Approximation by arbitrary nonlinear expressions; widths and entropy 41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX) 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems