Abstract:
This article is a study of the behaviour of widths describing the approximation properties of subspaces generated by the translates of $N$ fixed functions with respect to some lattice. A connection is established between the approximation characteristics and the geometric properties of $N$-fold packing of Lebesgue sets of a function depending on the metrics of the spaces in which the approximation is carried out. The concept of the mean dimension is introduced, and it is proved that the widths under study converge to the Kolmogorov widths of the same mean dimension.
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