Title | Estimates of the best m-term trigonometric approximations of classes of analytic functions |
Publication Type | Journal Article |
Year of Publication | 2015 |
Authors | Serdyuk, AS, Stepanyuk, TA |
Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
DOI | 10.15407/dopovidi2015.02.032 |
Issue | 2 |
Section | Mathematics |
Pagination | 32-37 |
Date Published | 2/2015 |
Language | Ukrainian |
Abstract | In the metrics of spaces $L_{s}$, $1\leq s\leq\infty$, we obtain exact in order estimates of the best $m$-term
trigonometric approximations of classes of the convolutions of periodic functions that belong to a unit ball of the space $L_{p}$, $1\leq p\leq\infty$, with the generating kernel $\Psi_{\beta}(t) =\textstyle\sum\limits_{k=1}^{\infty}\psi(k)\cos(kt-{\beta\pi}/{2})$, $\beta\in \mathbb{R}$, whose coefficients $\psi(k)$ tend to zero not slower than a geometric progression. The obtained estimates coincide in order with the approximation by Fourier sums of the given classes of functions in the Ls-metric. This fact allows us to write down exact order estimates of the best orthogonal trigonometric approximations and the trigonometric widths of the given classes. |
Keywords | analytic function, trigonometric approximation |
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