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.
Asymptotic behavior of the widths of classes of the generalized Poisson integralsA Serdyuk, I SokolenkoAlgebraic and Geometric Methods of Analysis, 102 2023
Asymptotic estimates for the widths of classes of functions of high smoothnessAS Serdyuk, IV SokolenkoarXiv preprint arXiv:2304.04586 2023
Мiжнародна конференцiя „теорiя наближення функцiй та її застосування”, присвячена 80-рiччю вiд дня народження члена-кореспондента НАН України, професора ОІ Степанця (1942–2007)I SokolenkoUkrains’ kyi Matematychnyi Zhurnal 74 (11), 1583-1584 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
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
Наближення сумами Фур’є на класах диференційовних у сенсі Вейля–Надя функцій із високим показником гладкостіAS Serdyuk, IV SokolenkoUkrains’ kyi Matematychnyi Zhurnal 74 (5), 685-700 2022
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
Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothnessAS Serdyuk, IV SokolenkoarXiv preprint arXiv:1906.02531 2019
Наближення інтерполяційними тригонометричними поліно- мами в метриках просторів на класах періодичних цілих функційAS Serdyuk, IV SokolenkoUkrains’ kyi Matematychnyi Zhurnal 71 (2), 283-292 2019
Approximation by Fourier sums and interpolation trigonometric polynomials in classes of differentiable functions with high exponents of smoothnessAS Serdyuk, IV Sokolenko 2019
ОЛЕКСАНДР ІВАНОВИЧ СТЕПАНЕЦЬ (до 75-річчя від дня народження)AS Romanyuk, VS Romanyuk, VV Savchuk, AM Samoilenko, AS Serdyuk, ...Ukrains’ kyi Matematychnyi Zhurnal 69 (5), 579-579 2017
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
Asymptotic equalities for best approximations for classes of infinitely differentiable functions defined by the modulus of continuityAS Serdyuk, IV SokolenkoMathematical Notes 99, 901-915 2016
Approximation by linear methods of classes of differentiable functionsAS Serdyuk, IV SokolenkoarXiv preprint arXiv:1303.1300 2013
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
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: 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
Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothnessAS Serdyuk, IV SokolenkoarXiv preprint arXiv:1906.02531 2019Citations: 13
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: 8
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: 8
Approximation by linear methods of classes of differentiable functionsAS Serdyuk, IV SokolenkoarXiv preprint arXiv:1303.1300 2013Citations: 6
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: 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
Наближення сумами Фур’є на класах диференційовних у сенсі Вейля–Надя функцій із високим показником гладкостіAS Serdyuk, IV SokolenkoUkrains’ kyi Matematychnyi Zhurnal 74 (5), 685-700 2022Citations: 3
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
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
