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Direct and Inverse Theorems in the Theory of Approximation of Functions in the Space Sp
We continue the investigation of approximation properties of the space Sp. We introduce the notion of kth modulus of continuity and establish direct and inverse theorems on approximation in the spaceExpand
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Approximation by fourier sums and best approximations on classes of analytic functions
We establish asymptotic equalities for upper bounds of approximations by Fourier sums and for the best approximations in the metrics of C and L1 on classes of convolutions of periodic functions thatExpand
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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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Lebesgue-type inequalities for the de la Vallée-poussin sums on sets of entire functions
For functions from the sets CψβLs, 1 ≤ s ≤ ∞, where ψ(k) > 0 and $ {\lim_{{k\to \infty }}}\frac{{\psi \left( {k+1} \right)}}{{\psi (k)}} $, we obtain asymptotically sharp estimates for the norms ofExpand
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Lebesgue-type inequalities for the de la Valée-Poussin sums on sets of analytic functions
For functions from the sets CβψC and CβψLs, 1 ≤ s ≤ 1, generated by sequences ψ(k) > 0 satisfying the d’Alembert condition $ {\lim_{{k\to \infty }}}\frac{{\psi \left( {k+1} \right)}}{{\psiExpand
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Linear approximation methods and the best approximations of the Poisson integrals of functions from the classes $ {H_{{\omega_p}}} $ in the metrics of the spaces Lp
We obtain upper estimates for the least upper bounds of approximations of the classes of Poisson integrals of functions from $ {H_{{\omega_p}}} $ for 1 ≤ p < ∞ by a certain linear method Un* in theExpand
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Asymptotic behavior of best approximations of classes of Poisson integrals of functions from Hω
TLDR
We find asymptotic formulas for the least upper bounds of approximation in the metric of the space C by using a linear method U"n^* for classes of Poisson integrals of continuous [email protected] functions in the case where their moduli of continuity do not exceed fixed convex majorants. Expand
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Widths and best approximations for classes of convolutions of periodic functions
We establish exact lower bounds for the Kolmogorov widths in the metrics ofC andL for classes of functions with high smoothness; the elements of these classes are sourcewise-representable asExpand
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Lower bounds for widths of classes of convolutions of periodic functions in the metrics ofC andL
We give new sufficient conditions for kernels to belong to the set Cy,2n introduced by Kushpel'. These conditions give the possibility of extending the set of kernels belonging to Cy,2n. On the basisExpand
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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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