Geodesic
Best Trigonometric and Bilinear Approximations of Classes of Functions of Several Variables
Matematičeskie zametki, Tome 94 (2013) no. 3, pp. 401-415

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Order-sharp estimates of the best orthogonal trigonometric approximations of the Nikolskii–Besov classes $B^{r}_{p,\theta}$ of periodic functions of several variables in the space $L_{q}$ are obtained. Also the orders of the best approximations of functions of $2d$ variables of the form $g(x,y)=f(x-y)$, $x,y\in \mathbb{T}^d=\prod_{j=1}^{d}[-\pi,\pi]$, $f(x)\in B^r_{p,\theta}$, by linear combinations of products of functions of $d$ variables are established.
Keywords: best trigonometric approximation of functions, best bilinear approximation of functions, Nikolskii–Besov class of periodic functions, the space $L_{q}$, Minkowski inequality.
Mots-clés : Fourier sum, Vallée-Poussin kernel 
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     author = {A. S. Romanyuk},
     title = {Best {Trigonometric} and {Bilinear} {Approximations} of {Classes} of {Functions} of {Several} {Variables}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {401--415},
     publisher = {mathdoc},
     volume = {94},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_94_3_a7/}
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A. S. Romanyuk. Best Trigonometric and Bilinear Approximations of Classes of Functions of Several Variables. Matematičeskie zametki, Tome 94 (2013) no. 3, pp. 401-415. http://geodesic.mathdoc.fr/item/MZM_2013_94_3_a7/