Abstract:
Asymptotic equalities are obtained for upper bounds of the deviations of Fourier sums in the classes of convolutions of Poisson kernels and continuous functions with moduli of continuity not exceeding fixed majorants.
Citation:
A. I. Stepanets, “Solution of the Kolmogorov–Nikol'skii problem for the Poisson integrals of continuous functions”, Sb. Math., 192:1 (2001), 113–139
\Bibitem{Ste01}
\by A.~I.~Stepanets
\paper Solution of the Kolmogorov--Nikol'skii problem for the~Poisson integrals of continuous functions
\jour Sb. Math.
\yr 2001
\vol 192
\issue 1
\pages 113--139
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\crossref{https://doi.org/10.1070/sm2001v192n01ABEH000538}
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Linking options:
https://www.mathnet.ru/eng/sm538
https://doi.org/10.1070/sm2001v192n01ABEH000538
https://www.mathnet.ru/eng/sm/v192/i1/p113
This publication is cited in the following 14 articles:
P. G. Potseiko, Y. A. Rovba, “The de la Vallée Poussin sums of Fourier–Chebyshev rational integral operators and approximations to Poisson integrals on the segment”, Siberian Math. J., 64:1 (2023), 137–156
P. G. Patseika, Ya. A. Rouba, “On rational approximations of Poisson integrals on the interval by Fejer sums of Fourier – Chebyshev integral operators”, Vescì Akademìì navuk Belarusì. Seryâ fizika-matematyčnyh navuk, 59:3 (2023), 183
P. G. Potseiko, Y. A. Rovba, “Approximations on classes of Poisson integrals by Fourier–Chebyshev rational integral operators”, Siberian Math. J., 62:2 (2021), 292–312
O. G. Rovenskaya, O. A. Novikov, “O priblizhenii srednimi Feiera klassov analiticheskikh periodicheskikh funktsii”, Chebyshevskii sb., 21:4 (2020), 218–226
O. G. Rovenskaya, “Priblizhenie analiticheskikh funktsii povtornymi summami Valle Pussena”, Kompyuternye issledovaniya i modelirovanie, 11:3 (2019), 367–377
Novikov O., Rovenska O., “Approximation of Classes of Poisson Integrals By Repeated Fejer Sums”, Lobachevskii J. Math., 38:3, SI (2017), 502–509
A. S. Serdyuk, I. V. Sokolenko, “Asymptotic Equalities for Best Approximations for Classes of Infinitely Differentiable Functions Defined by the Modulus of Continuity”, Math. Notes, 99:6 (2016), 901–915
O. G. Rovenskaya, O. A. Novikov, “Priblizhenie analiticheskikh periodicheskikh funktsii lineinymi srednimi ryadov Fure”, Chebyshevskii sb., 17:2 (2016), 170–183
O. A. Novikov, O. G. Rovenskaya, “Priblizhenie klassov integralov Puassona summami Feiera”, Kompyuternye issledovaniya i modelirovanie, 7:4 (2015), 813–819
A. S. Serdyuk, Ie. Yu. Ovsii, “Uniform Approximation of Periodical Functions by Trigonometric Sums of Special Type”, ISRN Mathematical Analysis, 2014 (2014), 1
A. S. Serdyuk, Ie. Yu. Ovsii, “Uniform approximation of Poisson integrals of functions from the class H ω by de la Vallée Poussin sums”, Anal Math, 38:4 (2012), 305
A.S. Serdyuk, I.V. Sokolenko, “Asymptotic behavior of best approximations of classes of Poisson integrals of functions from”, Journal of Approximation Theory, 2011
O. G. Rovenskaya, O. A. Novikov, “Approximation of Poisson integrals by repeated de la Vallée Poussin sums”, Nonlinear Oscill, 2010
A. S. Serdyuk, I. V. Sokolenko, “Linear approximation methods and the best approximations of the Poisson integrals of functions from the classes HωpHωp in the metrics of the spaces L p”, Ukr Math J, 2010
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