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arXiv · 2001.00374

Uniform approximations by Fourier sums on classes of convolutions of periodic functions

A. S. Serdyuk·T. A. Stepanyuk
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Abstract

We establish asymptotic estimates for exact upper bounds of uniform approximations by Fourier sums on the classes of $2π$-periodic functions, which are represented by convolutions of functions $φ(φ\bot 1)$ from unit ball of the space $L_{1}$ with fixed kernels $Ψ_β$ of the form $Ψ_β(t)=\sum\limits_{k=1}^{\infty}ψ(k) \cos\left(kt-\frac{βπ}{2}\right)$, $\sum\limits_{k=1}^{\infty}kψ(k)<\infty$, $ψ(k)\geq 0$, $β\in\mathbb{R}$.

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A. S. Serdyuk, T. A. Stepanyuk. 2020-01-02. Uniform approximations by Fourier sums on classes of convolutions of periodic functions. https://arxiv.org/abs/2001.00374

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