Approximation by Fourier sums and Kolmogorov widths for classes $\mathbf{MB}^\Omega_{p,\theta}$ of periodic functions of several variables

S. A. Stasyuk

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 247-257

Résumé

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 $L_q$.

Détail

Keywords: hyperbolic cross, Kolmogorov width, best approximation, mixed smoothness, Fourier sums.

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