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Estimates of the best approximations and approximations of Fourier sums of classes of convolutions of periodic functions of not high smoothness in integral metrics
In metric of spaces $L_{s}, \ 1< s\leq\infty$, we obtain exact order estimates of best approximations and approximations by Fourier sums of classes of convolutions the periodic functions that belongExpand
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Order estimations of the best approximations and approximations of the Fourier sums on the classes of infinitely differentiable functions
We obtained order estimations for the best uniform approximations by trigonometric polynomials and approximations by Fourier sums of classes of $2\pi$-periodic continuous functions, whichExpand
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Lebesque-type inequalities for the Fourier sums on classes of generalized Poisson integrals
For functions from the set of generalized Poisson integrals $C^{\alpha,r}_{\beta}L_{p}$, $1\leq p <\infty$, we obtain upper estimates for the deviations of Fourier sums in the uniform metric in termsExpand
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About Lebesgue inequalities on the classes of generalized Poisson integrals
For the functions $f$, which can be represented in the form of the convolution $f(x)=\frac{a_{0}}{2}+\frac{1}{\pi}\int\limits_{-\pi}^{\pi}\sum\limits_{k=1}^{\infty}e^{-\alphaExpand
Asymptotically best possible Lebesque-type inequalities for the Fourier sums on sets of generalized Poisson integrals
In this paper we establish Lebesgue-type inequalities for $2\pi$-periodic functions $f$, which are defined by generalized Poisson integrals of the functions $\varphi$ from $L_{p}$, $1\leq p< \infty$.Expand
Order estimates of the best orthogonal trigonometric approximations of classes of convolutions of periodic functions of not high smoothness
We obtain order estimates for the best uniform orthogonal trigonometric approximations of $2\pi$-periodic functions, whose $(\psi,\beta)$-derivatives belong to unit balls of spaces $L_{p}, \ 1\leqExpand
Construction of good polynomial lattice rules in weighted Walsh spaces by an alternative component-by-component construction
TLDR
We study the efficient construction of good polynomial lattice rules, which are special instances of quasi-Monte Carlo (QMC) methods. Expand
Estimates for approximations by Fourier sums, best approximations and best orthogonal trigonometric approximations of the classes of (\psi, \beta)-differentiable functions
We obtain the exact-order estimates for approximations by Fourier sums, best approximations and best orthogonal trigonometric approximations in metrics of spaces L_s, 1\leq s<\infty, of classes ofExpand
Component-by-component digit-by-digit construction of good polynomial lattice rules in weighted Walsh spaces
TLDR
We consider the efficient construction of polynomial lattice rules, which are special cases of so-called quasi-Monte Carlo (QMC) rules. Expand
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Estimates of the best m -term trigonometric approximations of classes of analytic functions
In metric of spaces $L_{s}, \ 1\leq s\leq\infty$, we obtain exact in order estimates of best $m$-term trigonometric approximations of classes of convolutions of periodic functions, that belong toExpand
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