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arXiv · 1410.3866

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

A. S. Serdyuk·T. A. Stepaniuk
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Abstract

In metric of spaces $L_{s}, \ 1\leq s\leq\infty$, 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 $L_{p}, \ 1\leq p\leq\infty$, with generated kernel $Ψ_β(t)=\sum\limits_{k=1}^{\infty}ψ(k)\cos(kt-\frac{βπ}{2})$, $β\in \mathbb{R}$, whose coefficients $ψ(k)$ 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.

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A. S. Serdyuk, T. A. Stepaniuk. 2014-10-14. Estimates of best $m$-term trigonometric approximation of classes of analytic functions. https://arxiv.org/abs/1410.3866

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