Uniform approximations by Fourier sums on classes of generalized Poisson integrals

2016/03/06 by Serdyuk, A. S., Stepaniuk, T. A. · 1 citation
#42A05 #42A10 #42A16 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1603.01891

Abstract

We find asymptotic equalities for exact upper bounds of approximations by Fourier sums in uniform metric on classes of 2π-periodic functions, representable in the form of convolutions of functions φ, which belong to unit balls of spaces L_p, with generalized Poisson kernels. For obtained asymptotic equalities we introduce the estimates of remainder, which are expressed in the explicit form via the parameters of the problem.

Cited by

• Estimates of deviations of Fourier sums on Weyl-Nagy classes W^r_β,1

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