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arXiv · 1310.8519

Estimations of the best approximations of classes of infinitely differentiable functions in uniform and integral metrics

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

We find uniform with respect to parameter $p \ (1\leq p\leq\infty)$ upper estimations of best approximations by trigonometric polynomials of classes $C^ψ_{β,p}$ of periodic functions generated by sequences $ψ(k)$, that decrease to nought faster than any power function. Obtained estimations are exact for order and have constants that are written in explicit form and depend on function $ψ$ only. We obtain analogical estimations for best approximations of classes $L^ψ_{β,1}$ in metrics of spaces $L_{s}$, $1\leq s\leq \infty$.

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A. S. Serdyuk, T. A. Stepaniuk. 2013-10-31. Estimations of the best approximations of classes of infinitely differentiable functions in uniform and integral metrics. https://arxiv.org/abs/1310.8519

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