Abstract:
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 $L_{q}$, Fourier sum, Vallée-Poussin kernel, Minkowski inequality.
Fulltext:
PDF file (518 kB)
