2019
Том 71
№ 9

All Issues

Shkapa V. V.

Articles: 2
Article (Ukrainian)

Best trigonometric and bilinear approximations for the classes of $(ψ, β)$ -differentiable periodic functions

Shkapa V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2016. - 68, № 3. - pp. 386-399

We establish the exact-order estimates for the best $m$-term trigonometric approximations of the classes $L^{\psi}_{\beta, 1}$ in the space $L_q,\; 2 < q < \infty$. We also determine the exact orders of the best bilinear approximations for the classes of functions of two variables generated by functions of a single variable from the class$L^{\psi}_{\beta, p}$ by the shifts of the argument in the space $L_{q_1,q_2},\; 1 \leq q_1,\; q_2 \leq \infty$.

Article (Ukrainian)

Approximating Characteristics of the Classes $L_{β,p}^{ψ}$ of Periodic Functions in the Space $L_q$

Shkapa V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2015. - 67, № 8. - pp. 1139-1150

We obtain the exact-order estimates of the best $m$-term and orthogonal trigonometric approximations and establish the order of trigonometric widths for the classes $L_{β,p}^{ψ}$ in the space $L_q$ for some relations between the parameters $p$ and $q$.