Geodesic
Best approximations and widths of classes of periodic functions of several variables
Sbornik. Mathematics, Tome 199 (2008) no. 2, pp. 253-275

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Order estimates are obtained for the best approximations of the Besov classes $B_{p,\theta}^r$ of periodic functions of several variables in the spaces $L_1$ and $L_\infty$ by trigonometric polynomials whose harmonic indices lie in step hyperbolic crosses. The orders of the orthoprojection widths of the classes $B_{p,\theta}^r$ and the linear widths of the classes $B_{p,\theta}^r$ and $W_{p,\alpha}^r$ in the space $L_1$ are found. Bibliography: 22 titles. 
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     author = {A. S. Romanyuk},
     title = {Best approximations and widths of classes of periodic functions of several variables},
     journal = {Sbornik. Mathematics},
     pages = {253--275},
     publisher = {mathdoc},
     volume = {199},
     number = {2},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2008_199_2_a4/}
}
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A. S. Romanyuk. Best approximations and widths of classes of periodic functions of several variables. Sbornik. Mathematics, Tome 199 (2008) no. 2, pp. 253-275. http://geodesic.mathdoc.fr/item/SM_2008_199_2_a4/