Uniform approximations by Fourier sums on classes of convolutions with generalized Poisson kernels

TitleUniform approximations by Fourier sums on classes of convolutions with generalized Poisson kernels
Publication TypeJournal Article
Year of Publication2016
AuthorsSerdyuk, AS, Stepanyuk, TA
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2016.11.010
Issue11
SectionMathematics
Pagination10-16
Date Published11/2016
LanguageUkrainian
Abstract

We find asymptotic unimprovable equalities for exact upper bounds of approximations by Fourier sums in a uniform
metric on the classes of 2π-periodic functions representable in the form of convolutions of functions φ, which belong
to unit balls of spaces Lp, with generalized Poisson kernels. For the obtained asymptotic equalities, we introduce the
estimate of a remainder, which is expressed in the explicit form via absolute constants and parameters of the problem.
This can be useful for practical application.
Keywordsasymptotic equality, Fourier sums, generalized Poisson kernels, Kolmogorov—Nikol'skii problem
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