Asymptotic estimates for the widths of classes of functions of high smothness A.S. Serdyuk and I.V. Sokolenko
Vasyl Stefanyk Precarpathian National University We find two-sided estimates for Kolmogorov, Bernstein, linear and projection widths of the classes of convolutions of $2\\pi$-periodic functions $\\varphi$, such that $\\|\\varphi\\|_2\\le1$, with fixed generated kernels $\\Psi_{\\bar{\\beta}}$, which have Fourier series of the form $$\\sum\\limits_{k=1}^\\infty \\psi(k)\\cos(kt-\\beta_k\\pi/2),$$ where $\\psi(k)\\ge0,$ $\\sum\\psi^2(k)<\\infty, \\beta_k\\in\\mathbb{R}$. It is shown that for rapidly decreasing sequences $\\psi(k)$ (in particular, if $\\lim\\limits_{k\\rightarrow\\infty}{\\psi(k+1)}/{\\psi(k)}=0$) the obtained estimates are asymptotic equalities. We establish that asymptotic equalities for widths of this classes are realized by trigonometric Fourier sums.
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Asymptotic estimates for the widths of classes of functions of high smoothnessAS Serdyuk, IV SokolenkoarXiv preprint arXiv:2304.04586 2023
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Approximation by Fourier sums in the classes of Weyl–Nagy differentiable functions with high exponent of smoothnessAS Serdyuk, IV SokolenkoUkrainian Mathematical Journal 74 (5), 783-800 2022
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On asymptotic equations for the widths of classes of the generalized Poisson integralsA Serdyuk, I Sokolenko 2021
Asymptotic estimates for the widths of classes of periodic functions of high smothnessA Serdyuk, I Sokolenko 2021
Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothnessAS Serdyuk, IV SokolenkoJournal of Mathematical Sciences 252, 526-540 2021
Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothnessAS Serdyuk, IV SokolenkoarXiv preprint arXiv:2008.01450 2020
Approximation by Interpolation Trigonometric Polynomials in Metrics of the Space Lp on the Classes of Periodic Entire Functions*AS Serdyuk, IV SokolenkoUkrainian Mathematical Journal 71 (2), 322-332 2019
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Approximation of classes of convolutions of periodic functions by linear methods constructed on basis of Fourier-Lagrange coefficientsAS Serdyuk, IV SokolenkoarXiv preprint arXiv:1703.09048 2017
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Approximation by linear methods of classes of differentiable functionsAS Serdyuk, IV SokolenkoarXiv preprint arXiv:1303.1300 2013
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MOST CITED SCHOLAR PUBLICATIONS
Соколенко IВ Рiвномiрнi наближення класiв (ψ, β)-диференцiйовних функцiй лiнiйними методамиАС СердюкТеорiя наближення функцiй та сумiжнi питання: Зб. праць Iн-ту математики НАН 2011Citations: 18
Asymptotic behavior of best approximations of classes of Poisson integrals of functions from HωAS Serdyuk, IV SokolenkoJournal of Approximation Theory 163 (11), 1692-1706 2011Citations: 17
Uniform approximation of the classes of (ψ, β)-differentiable functions by linear methods. Extremal Problems of the Theory of Functions and Related ProblemsAS Serdyuk, IV SokolenkoProc. Inst. Math. NAS Ukr 8 (1), 181-189 2011Citations: 16
Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothnessAS Serdyuk, IV SokolenkoarXiv preprint arXiv:1906.02531 2019Citations: 11
Asymptotic behavior of best approximations of classes of periodic analytic functions defined by moduli of continuityAS Serdyuk, IV SokolenkoProc. of the Bulgarian–Turkish–Ukrainian Sci. Conf.“Mathematical Analysis 2010Citations: 9
Approximation by Interpolation Trigonometric Polynomials in Metrics of the Space Lp on the Classes of Periodic Entire Functions*AS Serdyuk, IV SokolenkoUkrainian Mathematical Journal 71 (2), 322-332 2019Citations: 7
Approximation by of classes of (ψ, β)–differentiable functions by interpolation trigonometric polynomials, ZbAS Serdyuk, IV SokolenkoPr. Inst. Mat. NAN Ukr 13, 289-299 Citations: 7
Approximation by linear methods of classes of differentiable functionsAS Serdyuk, IV SokolenkoarXiv preprint arXiv:1303.1300 2013Citations: 5
Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothnessAS Serdyuk, IV SokolenkoJournal of Mathematical Sciences 252, 526-540 2021Citations: 4
Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothnessAS Serdyuk, IV SokolenkoarXiv preprint arXiv:2008.01450 2020Citations: 4
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Asymptotic equalities for best approximations for classes of infinitely differentiable functions defined by the modulus of continuityAS Serdyuk, IV SokolenkoMathematical Notes 99, 901-915 2016Citations: 3
The best approximation of Poisson integrals of functions from the class HωAS Serdyuk, IV SokolenkoDopov. Nats. Akad. Nauk Ukr 2, 33-37 2010Citations: 3
Approximation by Fourier sums in the classes of Weyl–Nagy differentiable functions with high exponent of smoothnessAS Serdyuk, IV SokolenkoUkrainian Mathematical Journal 74 (5), 783-800 2022Citations: 2
Linear approximation methods and the best approximations of the Poisson integrals of functions from the classes in the metrics of the spaces L pAS Serdyuk, IV SokolenkoUkrainian Mathematical Journal 62 (7), 1139-1157 2010Citations: 2
Approximation of classes of convolutions of periodic functions by linear methods constructed on basis of Fourier-Lagrange coefficientsAS Serdyuk, IV SokolenkoarXiv preprint arXiv:1703.09048 2017Citations: 1
Approximation of the-integrals of functions defined on the real axis by Fourier operatorsOI Stepanets’, IV SokolenkoUkrainian Mathematical Journal 56 (7), 1144-1150 2004Citations: 1
