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Approximation by Fourier sums on the classes of generalized Poisson integrals
Anatoly Serdyuk, Tetiana Stepaniuk
We present a survey of results related to the solution of Kolmogorov--Nikolsky problem for Fourier sums on the classes of generalized Poisson integrals , which consi…
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…
Lebesque-type inequalities for the Fourier sums on classes of generalized Poisson integrals
Anatoly Serdyuk, Tetiana Stepaniuk
For functions from the set of generalized Poisson integrals , , we obtain upper estimates for the deviations of Fourier sums in the uniform metric…
Uniform approximations by Fourier sums on classes of generalized Poisson integrals
A. S. Serdyuk, T. A. Stepaniuk
We find asymptotic equalities for exact upper bounds of approximations by Fourier sums in uniform metric on classes of -periodic functions, representable in the form of convolu…