Estimates of the best m-term trigonometric approximations of classes of analytic functions

TitleEstimates of the best m-term trigonometric approximations of classes of analytic functions
Publication TypeJournal Article
Year of Publication2015
AuthorsSerdyuk, AS, Stepanyuk, TA
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2015.02.032
Issue2
SectionMathematics
Pagination32-37
Date Published2/2015
LanguageUkrainian
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.
Keywordsanalytic function, trigonometric approximation
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