Order estimations of the best approximations and approximations of the Fourier sums on the classes of infinitely differentiable functions

A. S. Serdyuk; T. A. Stepaniuk

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arXiv · 1304.7379

Order estimations of the best approximations and approximations of the Fourier sums on the classes of infinitely differentiable functions

A. S. Serdyuk·T. A. Stepaniuk

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Abstract

We obtained order estimations for the best uniform approximations by trigonometric polynomials and approximations by Fourier sums of classes of $2π$-periodic continuous functions, which $(ψ,β)$-derivatives $f_β^ψ$ belong to unit balls of spaces $L_{p}, 1\leq p<\infty$ in case at consequences $ψ(k)$ decrease to nought faster than any power function. We also established the analogical estimations in $L_{s}$-metric, $1<s\leq\infty$, for classes of the summable $(ψ,β)$-differentiable functions, such that $\parallel f_β^ψ\parallel_{1}\leq1$.

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BibTeX RIS

A. S. Serdyuk, T. A. Stepaniuk. 2013-04-27. Order estimations of the best approximations and approximations of the Fourier sums on the classes of infinitely differentiable functions. https://arxiv.org/abs/1304.7379

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