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

Abstract

We establish asymptotic estimates for exact upper bounds of uniform approximations by Fourier sums on the classes of $2\pi$-periodic functions, which are represented by convolutions of functions $\phi (\phi \perp 1)$ from unit ball of the space $L_1$ with fixed kernels ${\Psi }_{\beta }$ of the form ${\Psi }_{\beta }(t)=\sum _{k=1}^{\infty }\psi (k)\cos \left(kt-\frac{\beta \pi }{2}\right)$, $\sum _{k=1}^{\infty }k\psi (k)<\infty$, $\psi (k)\ge 0$, $\beta \in \mathbb{R}$.