arXiv subjects
Publications and source records attributed to Andriy L. Shidlich.
We obtain the exact values of some important approximative quantities (such as, the best approximation, the basis width, Kolmogorov's width and the best $n$-term approximation) of certain sets of images of the diagonal operators in the Orlicz sequence spaces $l_M$.
We obtain order estimates in the spaces $L_p$ of the best $n$-term trigonometric orthogonal approximations of the classes ${\cal F}_{q}^ψ$ of periodic functions, whose Fourier coefficients decrease faster then any power function. We also obtain order estimates of the quantities of approximations by $n$-term Greedy approximants of such classes in the spaces $L_p$.
We find the exact order estimates of the approximations of the classes ${\cal F}_{q,r}^ψ$ of functions of several variables by greedy approximants in the integral metric. We also obtain the exact order estimates of the best $n$-term orthogonal trigonometric approximations of the classes ${\cal F}_{q,r}^ψ$ in the integral metric.
In the spaces $S^p$ of functions of several variables, $2π$-periodic in each variable, we study the approximative properties of operators $A^\vartriangle_{\varrho,r}$ and $P^\vartriangle_{\varrho,s}$, which generate two summation methods of multiple Fourier series on triangular regions. In particular, in the terms of approximation estimates of these operators, we give a constructive description of classes of functions, whose generalized derivatives belong to the classes $S^pH_ω$.