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arXiv · 1812.06475

Order estimates of best orthogonal trigonometric approximations of classes of infinitely differentiable functions

Tetiana Stepanyuk
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Abstract

In this paper we establish exact order estimates for the best uniform orthogonal trigonometric approximations of the classes of $2\pi$-periodic functions, whose $(\psi,\beta)$-derivatives belong to unit balls of spaces $L_{p}$, $1\leq p<\infty$, in the case, when the sequence $\psi(k)$ tends to zero faster, than any power function, but slower than geometric progression. Similar estimates are also established in the $L_{s}$-metric, $1<s\leq\infty$ for the classes of differentiable functions, which $(\psi,\beta)$-derivatives belong to unit ball of space $L_{1}$.

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Tetiana Stepanyuk. 2018-12-16. Order estimates of best orthogonal trigonometric approximations of classes of infinitely differentiable functions. https://arxiv.org/abs/1812.06475

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