arXiv subjects

A. P. Musienko

Publications and source records attributed to A. P. Musienko.

3 recordsLinked to original sources

arXiv2013

Lebesgue-type inequalities for de la Vallee Poussin sums and their interpolation analogues on the sets $(ψ,\barβ)$-differentiable functions

We obtain the estimates of steady rates of deviations of the de Vallée Poussin sums and interpolation analogues of sums of Vallée Poussin from the functions that belong to the space $C_{\barβ}^ψL_s, \ 1\leq s\leq\infty$ and are represented through the best approximations of $(ψ,\barβ)$-differentiable functions of this sort by trigonometric polynomials in the metric $L_s$

math.CA↗

arXiv2012

Lebesgue-type inequalities for de la Vallee Poussin sums on the sets of analytic and entire functions

For the functions from sets $C_β^ψC$ and $C_β^ψL_s, \ 1\leq s\leq\infty$, generated by sequences $ψ(k)>0$ satisfying the condition d'Alembert $\mathop {\rm \lim}\limits_{k\rightarrow\infty}\frac{ψ(k+1)}{ψ(k)}=q, \ q\in[0,1)$, asymptotically unimprovable estimates for deviations of de la Vallée Poussin sums in the uniform metric, which are represented in terms of values of the best approximations of $(ψ,β)$-differentiable functions of this sort by trigonometric polynomials in the metrics $L_s$ are obtained. Proved that received estimates are unimprovable on some important functional subsets.

math.CA↗

arXiv2011

Approximation of classes of analytic functions by de la Vallee Poussin sums in uniform metric

In this paper asymptotic equalities are found for the least upper bounds of deviations in the uniform metric of de la Vallee Poussin sums on classes of 2π-periodic (ψ,β)-differentiable functions admitting an analytic continuation into the given strip of the complex plane. As a consequence, asymptotic equalities are obtained on classes of convolutions of periodic functions generated by the Neumann kernel and the polyharmonic Poisson kernel.

math.CA↗