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math.CA2020★ 2 cited
About Lebesgue inequalities on the classes of generalized Poisson integrals
A. S. Serdyuk, T. A. Stepaniuk
For the functions , which can be represented in the form of the convolution $f(x)=\frac{a_{0}}{2}+\frac{1}π\int\limits_{-π}^π\sum\limits_{k=1}^{\infty}e^{-αk^{r}}\cos(kt-\frac{β…
math.CA2020
Uniform approximations by Fourier sums on classes of convolutions of periodic functions
A. S. Serdyuk, T. A. Stepanyuk
We establish asymptotic estimates for exact upper bounds of uniform approximations by Fourier sums on the classes of -periodic functions, which are represented by convolutions…