Search Results - "Serdyuk, A.S."

Asymptotic estimates for the widths of classes of functions of high smothness by Serdyuk, A.S., Sokolenko, I.V.

“…We find two-sided estimates for Kolmogorov, Bernstein, linear and projection widths of the classes of convolutions of $2\pi$-periodic functions $\varphi$, such…”
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Direct and inverse theorems on the approximation of almost periodic functions in Besicovitch-Stepanets spaces by Serdyuk, A.S., Shidlich, A.L.

“…Direct and inverse approximation theorems are proved in the Besicovitch-Stepanets spaces $B{\mathcal S}^{p}$ of almost periodic functions in terms of the best…”
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Order estimates of the uniform approximations by Zygmund sums on the classes of convolutions of periodic functions by Serdyuk, A.S., Hrabova, U.Z.

“…The Zygmund sums of a function $f\in L_{1}$ are trigonometric polynomials of the form…”
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APPROXIMATION BY INTERPOLATION TRIGONOMETRIC POLYNOMIALS IN METRICS OF THE SPACE [L.sub.p] ON THE CLASSES OF PERIODIC ENTIRE FUNCTIONS by Serdyuk, A.S, Sokolenko, I.V

“…We establish asymptotic equalities for the least upper bounds of approximations by interpolation trigonometric polynomials with equidistant distribution of…”
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WIDTHS OF FUNCTIONAL CLASSES DEFINED BY THE MAJORANTS OF GENERALIZED MODULI OF SMOOTHNESS IN THE SPACES [S.sup.p] by Abdullayev, F.G, Serdyuk, A.S, Shidlich, A.L

“…We obtain exact Jackson-type inequalities in terms of the best approximations and averaged values of the generalized moduli of smoothness in the spaces…”
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APPROXIMATION OF THE CLASSES OF GENERALIZED POISSON INTEGRALS BY FOURIER SUMS IN METRICS OF THE SPACES [L.sub.S] by Serdyuk, A.S, Stepanyuk, T.A

“…In metrics of the spaces Ls, 1 [less than or equal to] s [less than or equal to] [infinity], we establish asymptotic equalities for the upper bounds of…”
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Uniform approximations by Fourier sums on classes of convolutions with generalized Poisson kernels by Serdyuk, A.S., Stepanyuk, T.A.

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Approximation by Fourier Sums in the Classes of Weyl–Nagy Differentiable Functions with High Exponent of Smoothness by Serdyuk, A. S., Sokolenko, I. V.

“…We establish asymptotic estimates for the least upper bounds of approximations in the uniform metric by Fourier sums of order n − 1 in the classes of…”
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Estimates of the best orthogonal trigonometric approximations of the classes of convolutions of periodic functions of not high smoothness by Serdyuk, A.S., Stepaniuk, T.A.

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Estimates of the best m-term trigonometric approximations of classes of analytic functions by Serdyuk, A.S., Stepanyuk, T.A.

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Approximation by interpolation trigonometric polynomials on classes of periodic analytic functions by Serdyuk, A. S.

“…We establish asymptotically unimprovable interpolation analogs of Lebesgue-type inequalities on the sets of ( ψ , β )-differentiable functions generated by…”
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Estimations of the Best Approximations for the Classes of Infinitely Differentiable Functions in Uniform and Integral Metrics by Serdyuk, A. S., Stepanyuk, T. A.

“…We establish uniform (with respect to the parameter p , 1 ≤ p ≤ ∞) upper estimations of the best approximations by trigonometric polynomials for the classes C…”
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Oleksandr Ivanovych Stepanets (on his 80th birthday) by Lukovs'kyi, I.O, Makarov, V.L, Tymokha, O.M, Motornyi, V.P, Shevchuk, I.O, Holub, A.P, Zaderei, P.V, Romanyuk, A.S, Savchuk, V.V, Serdyuk, A.S, Sokolenko, I.V, Shydlich, A.L

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Lebesgue-type inequalities for the de la Valée-Poussin sums on sets of analytic functions by Musienko, A. P., Serdyuk, A. S.

“…For functions from the sets C β ψ C and C β ψ L s , 1 ≤  s  ≤ 1, generated by sequences ψ( k ) > 0 satisfying the d’Alembert condition , we obtain…”
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Lebesgue-type inequalities for the de la Vallée-poussin sums on sets of entire functions by Musienko, A. P., Serdyuk, A. S.

“…For functions from the sets C ψ β L s , 1 ≤  s  ≤ ∞, where ψ( k ) > 0 and , we obtain asymptotically sharp estimates for the norms of deviations of the de la…”
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Exact values of Kolmogorov widths of classes of Poisson integrals by Serdyuk, A.S., Bodenchuk, V.V.

“…We prove that the Poisson kernel Pq,β(t)=∑k=1∞qkcos(kt−βπ2), q∈(0,1), β∈R, satisfies Kushpel’s condition Cy,2n beginning with a number nq where nq is the…”
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Order Estimates for the Best Orthogonal Trigonometric Approximations of the Classes of Convolutions of Periodic Functions of Low Smoothness by Serdyuk, A. S., Stepanyuk, T. A.

“…We establish order estimates for the best uniform orthogonal trigonometric approximations on the classes of 2π-periodic functions whose ( ψ, β )-derivatives…”
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Exact Values of Kolmogorov Widths for the Classes of Analytic Functions. I by Bodenchuk, V. V., Serdyuk, A. S.

“…We prove that the kernels of analytic functions of the form H h , β t = ∑ k = 1 ∞ 1 cosh k h cos k t − β π 2 , h > 0 , β ∈ ℝ , satisfy Kushpel’s condition C y,…”
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Igor Oleksandrovych Shevchuk (on His 75th Birthday) by Lukovskyi, I.O, Makarov, V.L, Perestyuk, M.O, Tymokha, O.M, Boichuk, O.A, Gutlyanskyi, V.Ya, Kochubei, A.N, Motornyi, V.P, Holub, A.P, Dzyubenko, G.A, Kovtunets, V.V, Nesterenko, O.N, Romanyuk, A.S, Serdyuk, A.S, Torbin, G.M

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Exact Values of Kolmogorov Widths for the Classes of Analytic Functions. II by Bodenchuk, V. V., Serdyuk, A. S.

“…It is shown that the lower bounds of the Kolmogorov widths d 2 n in the space C established in the first part of our work for the function classes that can be…”
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