2017
Том 69
№ 7

All Issues

On the best polynomial approximation in the space L2 and widths of some classes of functions

Vakarchuk S. B., Zabutnaya V. I.

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Abstract

We consider the problem of the best polynomial approximation of $2\pi$-periodic functions in the space $L_2$ in the case where the error of approximation $E_{n-1}(f)$ is estimated in terms of the $k$th-order modulus of continuity $\Omega_k(f)$ in which the Steklov operator $S_h f$ is used instead of the operator of translation $T_h f (x) = f(x + h)$. For the classes of functions defined using the indicated smoothness characteristic, we determine the exact values of different $n$-widths.

English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 8, pp 1168-1176.

Citation Example: Vakarchuk S. B., Zabutnaya V. I. On the best polynomial approximation in the space L2 and widths of some classes of functions // Ukr. Mat. Zh. - 2012. - 64, № 8. - pp. 1025-1032.

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