Estimates of best $m$-term trigonometric approximation of classes of analytic functions

Abstract

In metric of spaces $L_s,1\le s\le \infty$, we obtain exact in order estimates of best $m$-term trigonometric approximations of classes of convolutions of periodic functions, that belong to unit all of space $L_p,1\le p\le \infty$, with generated kernel ${\Psi }_{\beta }(t)=\sum _{k=1}^{\infty }\psi (k)\cos (kt-\frac{\beta \pi }{2})$, $\beta \in \mathbb{R}$, whose coefficients $\psi (k)$ tend to zero not slower than geometric progression. Obtained estimates coincide in order with approximation by Fourier sums of the given classes of functions in $L_s$-metric. This fact allows to write down exact order estimates of best orthogonal trigonometric approximation and trigonometric widths of given classes.

arXiv comment7 pages, in Ukrainian