Том 71
№ 4

All Issues

Zabutnaya V. I.

Articles: 1
Article (Russian)

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

Vakarchuk S. B., Zabutnaya V. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 8. - pp. 1025-1032

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.