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

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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 $$\Psi_{\beta}(t)=\sum\limits_{k=1}^{\infty}\psi(k)\cos(kt-\frac{\beta\pi}{2})$$, $$\beta\in \mathbb{R}$$, 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.

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###### Journal
2014-10-14
1410.3866