Geodesic
Approximation by Fourier sums and Kolmogorov widths for classes $\mathbf{MB}^\Omega_{p,\theta}$ of periodic functions of several variables
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 247-257

Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain exact order estimates for approximations of mixed smoothness classes $\mathbf{MB}^\Omega_{p,\theta}$ by Fourier sums in the metric $L_q$ for $1$. The spectrum of approximation polynomials lies in the sets generated by level surfaces of the function $\Omega(t)/\prod_{j=1}^dt_j^{1/p-1/q}$. Under some matching conditions on the parameters $p,q$ and $\theta$, we obtain exact order estimates for Kolmogorov widths of the classes under consideration in the metric $L_q$.
Keywords: hyperbolic cross, Kolmogorov width, best approximation, mixed smoothness, Fourier sums. 
@article{TIMM_2014_20_1_a23,
     author = {S. A. Stasyuk},
     title = {Approximation by {Fourier} sums and {Kolmogorov} widths for classes $\mathbf{MB}^\Omega_{p,\theta}$ of periodic functions of several variables},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {247--257},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a23/}
}
TY  - JOUR
AU  - S. A. Stasyuk
TI  - Approximation by Fourier sums and Kolmogorov widths for classes $\mathbf{MB}^\Omega_{p,\theta}$ of periodic functions of several variables
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2014
SP  - 247
EP  - 257
VL  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a23/
LA  - ru
ID  - TIMM_2014_20_1_a23
ER  - 
%0 Journal Article
%A S. A. Stasyuk
%T Approximation by Fourier sums and Kolmogorov widths for classes $\mathbf{MB}^\Omega_{p,\theta}$ of periodic functions of several variables
%J Trudy Instituta matematiki i mehaniki
%D 2014
%P 247-257
%V 20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a23/
%G ru
%F TIMM_2014_20_1_a23
S. A. Stasyuk. Approximation by Fourier sums and Kolmogorov widths for classes $\mathbf{MB}^\Omega_{p,\theta}$ of periodic functions of several variables. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 247-257. http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a23/