# Linear widths of Hölder-Nikol'skii classes of periodic functions of several variables

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## Abstract

We consider the linear widths λ_{ N }(*W* _{p} ^{r} (T^{n}), L_{q}) and λ_{ N }(*H* _{p} ^{r} (T^{n}), L_{q}) of the classes*W* _{p} ^{r} (T^{n}) and*H* _{p} ^{r} (T^{n}) of periodic functions of one or several variables in the space*L*_{q}. For the Sobolev classes*W* _{p} ^{r} (T^{n}) of functions of one or several variables, we state some well-known results without proof; for the Hölder-Nikol'skii classes*H* _{p} ^{r} (T^{n}), we state some well-known results, prove some new results, and present some previously unpublished proofs.

## Keywords

Periodic Function Linear Width Unpublished Proof Skii Class
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© Plenum Publishing Corporation 1996