Estimates of deviations of Fourier sums on Weyl–Nagy classes Wr β A.S. Serdyuk, I.V. Sokolenko Researches in Mathematics, 2025 We establish estimates for exact upper bounds of deviations of partial Fourier sums $S_{n-1}(f)$ on classes $W^r_{\\beta,1}, r>2, \\beta\\in\\mathbb{R},$ of $2\\pi$-periodic functions whose $(r,\\beta)$-derivatives in the Weyl-Nagy sense belong to the unit ball of the space $L_1$. The specified estimates allow us to write asymptotic equalities for the quantities $\\sup\\limits_{f\\in W^r_{\\beta,1}}|f(x)-S_{n-1}(f;x)|$ as $n\\rightarrow\\infty$, $r\\rightarrow\\infty$ for arbitrary relations between the parameters $r$ and $n$.
Asymptotic estimates for the widths of classes of functions of high smothness A.S. Serdyuk, I.V. Sokolenko Carpathian Mathematical Publications, 2023 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.
Approximation by fourier sums in classes of differentiable functions with high exponents of smoothness Methods of Functional Analysis and Topology, 2019
Asymptotic behavior of the widths of classes of the generalized Poisson integrals A Serdyuk, I Sokolenko Algebraic and Geometric Methods of Analysis, 102 , 2023 2023
Asymptotic estimates for the widths of classes of functions of high smoothness AS Serdyuk, IV Sokolenko arXiv preprint arXiv:2304.04586 , 2023 2023
Мiжнародна конференцiя „теорiя наближення функцiй та її застосування”, присвячена 80-рiччю вiд дня народження члена-кореспондента НАН України, професора ОІ Степанця (1942–2007) І Соколенко Ukrains’ kyi Matematychnyi Zhurnal 74 (11), 1583-1584 , 2022 2022
OLEKSANDR IVANOVYCH STEPANETS (on his 80th birthday) IO Lukovs' kyi, VL Makarov, OM Tymokha, VP Motornyi, IO Shevchuk, ... UKRAINIAN MATHEMATICAL JOURNAL 74 (5), 661-663 , 2022 2022
Approximation by Fourier sums in the classes of Weyl–Nagy differentiable functions with high exponent of smoothness AS Serdyuk, IV Sokolenko Ukrainian Mathematical Journal 74 (5), 783-800 , 2022 2022 Citations: 9
Наближення сумами Фур’є на класах диференційовних у сенсі Вейля–Надя функцій із високим показником гладкості AS Serdyuk, IV Sokolenko Ukrains’ kyi Matematychnyi Zhurnal 74 (5), 685-700 , 2022 2022
On asymptotic equations for the widths of classes of the generalized Poisson integrals A Serdyuk, I Sokolenko 2021
Asymptotic estimates for the widths of classes of periodic functions of high smothness A Serdyuk, I Sokolenko 2021
Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothness AS Serdyuk, IV Sokolenko Journal of Mathematical Sciences 252 (4), 526-540 , 2021 2021 Citations: 8
Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothness AS Serdyuk, IV Sokolenko arXiv preprint arXiv:2008.01450 , 2020 2020 Citations: 4
Approximation by Interpolation Trigonometric Polynomials in Metrics of the Space L p on the Classes of Periodic Entire Functions * AS Serdyuk, IV Sokolenko Ukrainian Mathematical Journal 71 (2), 322-332 , 2019 2019 Citations: 9
Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness AS Serdyuk, IV Sokolenko arXiv preprint arXiv:1906.02531 , 2019 2019 Citations: 17
Approximation by Fourier sums and interpolation trigonometric polynomials in classes of differentiable functions with high exponents of smoothness AS Serdyuk, IV Sokolenko Algebraic and Geometric Methods of Analysis, 54 , 2019 2019
Наближення інтерполяційними тригонометричними поліно- мами в метриках просторів на класах періодичних цілих функцій AS Serdyuk, IV Sokolenko Ukrains’ kyi Matematychnyi Zhurnal 71 (2), 283-292 , 2019 2019
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MOST CITED SCHOLAR PUBLICATIONS
Uniform approximation of classes of $$$(\psi,\bar\beta) $$$-differentiable functions by linear methods AS Serdyuk, IV Sokolenko Approximation Theory of Functions and Related Problems, Zb. prac’Inst. mat … , 2011 2011.0 Citations: 22
Asymptotic behavior of best approximations of classes of Poisson integrals of functions from Hω AS Serdyuk, IV Sokolenko Journal of Approximation Theory 163 (11), 1692-1706 , 2011 2011.0 Citations: 18
Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness AS Serdyuk, IV Sokolenko arXiv preprint arXiv:1906.02531 , 2019 2019.0 Citations: 17
Соколенко IВ Рiвномiрнi наближення класiв (ψ, β)-диференцiйовних функцiй лiнiйними методами АС Сердюк Теорiя наближення функцiй та сумiжнi питання: Зб. праць Iн-ту математики НАН … , 2011 2011.0 Citations: 16
Approximation by Fourier sums in the classes of Weyl–Nagy differentiable functions with high exponent of smoothness AS Serdyuk, IV Sokolenko Ukrainian Mathematical Journal 74 (5), 783-800 , 2022 2022.0 Citations: 9
Approximation by Interpolation Trigonometric Polynomials in Metrics of the Space L p on the Classes of Periodic Entire Functions * AS Serdyuk, IV Sokolenko Ukrainian Mathematical Journal 71 (2), 322-332 , 2019 2019.0 Citations: 9
Approximation by linear methods of classes of differentiable functions AS Serdyuk, IV Sokolenko arXiv preprint arXiv:1303.1300 , 2013 2013.0 Citations: 9
Approximation by of classes of (ψ, β)–differentiable functions by interpolation trigonometric polynomials, Zb AS Serdyuk, IV Sokolenko Pr. Inst. Mat. NAN Ukr 13, 289-299 , 0 Citations: 9
Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothness AS Serdyuk, IV Sokolenko Journal of Mathematical Sciences 252 (4), 526-540 , 2021 2021.0 Citations: 8
Asymptotic behavior of best approximations of classes of periodic analytic functions defined by moduli of continuity AS Serdyuk, IV Sokolenko Proc. of the Bulgarian–Turkish–Ukrainian Sci. Conf.“Mathematical Analysis … , 2010 2010.0 Citations: 8
Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothness AS Serdyuk, IV Sokolenko arXiv preprint arXiv:2008.01450 , 2020 2020.0 Citations: 4
Linear approximation methods and the best approximations of the Poisson integrals of functions from the classes in the metrics of the spaces L p AS Serdyuk, IV Sokolenko Ukrainian Mathematical Journal 62 (7), 1139-1157 , 2010 2010.0 Citations: 4
Asymptotic equalities for best approximations for classes of infinitely differentiable functions defined by the modulus of continuity AS Serdyuk, IV Sokolenko Mathematical Notes 99 (5), 901-915 , 2016 2016.0 Citations: 3
The best approximation of Poisson integrals of functions from the class Hω AS Serdyuk, IV Sokolenko Dopov. Nats. Akad. Nauk Ukr 2, 33-37 , 2010 2010.0 Citations: 3
Approximation of classes of convolutions of periodic functions by linear methods constructed on basis of Fourier-Lagrange coefficients AS Serdyuk, IV Sokolenko arXiv preprint arXiv:1703.09048 , 2017 2017.0 Citations: 2
Approximation of the-integrals of functions defined on the real axis by Fourier operators OI Stepanets’, IV Sokolenko Ukrainian Mathematical Journal 56 (7), 1144-1150 , 2004 2004.0 Citations: 1
Estimates of deviations of Fourier sums on Weyl-Nagy classes AS Serdyuk, IV Sokolenko arXiv preprint arXiv:2509.15769 , 2025 2025.0
UKRAINS’KYI MATEMATYCHNYI ZHURNAL VP MOTORNY, IO SHEVCHUK, SB VAKARCHUK, AO KORENOVSKYI, ... UKRAINS’KYI MATEMATYCHNYI ZHURNAL Учредители: Institute of Mathematics … , 2024 2024.0
Владислав Федорович Бабенко (до 75-річчя від дня народження) ВП Моторний, ІО Шевчук, СБ Вакарчук, АО Кореновський, ВО Кофанов, ... Ukrains’ kyi Matematychnyi Zhurnal 76 (10), 1565-1568 , 2024 2024.0
Uniform approximation by Fourier sums in Weyl–Nagy Uniform approximation by Fourier sums in Weyl–Nagy classes W A Serdyuk, I Sokolenko 2024.0
