arXiv subjects

U. Z. Grabova

Publications and source records attributed to U. Z. Grabova.

3 recordsLinked to original sources

arXiv2014

Approximation of classes of convolutions of periodic functions by Zygmund sums in integral metrics

We obtain estimates exact in order for deviations of Zygmund sums in metrics of spaces $L_{q}$, $1<q<\infty$, on classes of $2π$-periodic functions, that admit the representation in the form of convolution of functions that belong to unit ball of the space $L_{1}$ with fixed kernel $Ψ_β$. We show that at certain values of the parameters that define the class $L^ψ_{β,1}$ and method of approximation, Zygmund sums provide the order of best approximation of given classes by trigonometric polynomials in metric $L_{q}$

math.CA↗

arXiv2013

Estimates of the uniform approximations by Zygmund sums on the classes of convolutions of periodic functions

We obtain order-exact estimates for uniform approximations by using Zygmund sums $Z^{s}_{n}$ of classes $C^ψ_{β,p}$ of $2π$-periodic continuous functions $f$ representable by convolutions of functions from unit balls of the space $L_{p}$, $1< p<\infty$, with a fixed kernels $Ψ_β\in L_{p'}$, $\frac{1}{p}+\frac{1}{p'}=1$. In addition, we find a set of allowed values of parameters (that define the class $C^ψ_{β,p}$ and the linear method $Z^{s}_{n}$) for which Zygmund sums and Fejer sums realize the order of the best uniform approximations by trigonometric polynomials of those classes.

math.CA↗

arXiv2013

Order estimation of the best approximations and of the approximations by Fourier sums of classes of $(ψ,β)$--diferentiable functions

There were established the exact-order estimations of the best uniform approximations byψ the trigonometrical polynoms on the $C^ψ_{β,p}$ classes of $2π$-periodic continuous functions $f$, which are defined by the convolutions of the functions, which belong to the unit ball in $L_p$, $1\leq p <\infty$ spaces with generating fixed kernels $Ψ_β\subset|L_{p'}$, $\frac{1}{p}+\frac{1}{p'}=1$, whose Fourier coeficients decreasing to zero approximately as power functions. The exact order estimations were also established in $L_p$-metrics, $1 < p \leq\infty$ for $L^ψ_{β,1}$ classes of $2π$-periodic functions $f$, which are equivalent by means of Lebesque measure to the convolutions of $Ψ_β\subset|L_{p}$ kernels with the functions that belong to the unit ball in $L_1$ space. We showed that in investigating cases the orders of best approximations are realized by Fourier sums.

math.CA↗