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Mat. Sb., 2001, Volume 192, Number 1, Pages 113–138 (Mi msb538)  

This article is cited in 9 scientific papers (total in 9 papers)

Solution of the Kolmogorov–Nikol'skii problem for the Poisson integrals of continuous functions

A. I. Stepanets

Institute of Mathematics, Ukrainian National Academy of Sciences

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.

DOI: https://doi.org/10.4213/sm538

Full text: PDF file (346 kB)
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English version:
Sbornik: Mathematics, 2001, 192:1, 113–139

Bibliographic databases:

UDC: 517.5
MSC: Primary 42A10; Secondary 42A85
Received: 11.01.2000

Citation: A. I. Stepanets, “Solution of the Kolmogorov–Nikol'skii problem for the Poisson integrals of continuous functions”, Mat. Sb., 192:1 (2001), 113–138; Sb. Math., 192:1 (2001), 113–139

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. O. G. Rovenskaya, O. A. Novikov, “Approximation of Poisson integrals by repeated de la Vallée Poussin sums”, Nonlinear Oscill, 2010  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    2. A. S. Serdyuk, I. V. Sokolenko, “Linear approximation methods and the best approximations of the Poisson integrals of functions from the classes $ {H_{{\omega_p}}} $ in the metrics of the spaces L p”, Ukr Math J, 2010  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    3. A.S. Serdyuk, I.V. Sokolenko, “Asymptotic behavior of best approximations of classes of Poisson integrals of functions from”, Journal of Approximation Theory, 2011  crossref  mathscinet  isi  scopus  scopus  scopus
    4. 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  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    5. A. S. Serdyuk, Ie. Yu. Ovsii, “Uniform Approximation of Periodical Functions by Trigonometric Sums of Special Type”, ISRN Mathematical Analysis, 2014 (2014), 1  crossref  mathscinet  zmath
    6. O. A. Novikov, O. G. Rovenskaya, “Priblizhenie klassov integralov Puassona summami Feiera”, Kompyuternye issledovaniya i modelirovanie, 7:4 (2015), 813–819  mathnet
    7. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    8. O. G. Rovenskaya, O. A. Novikov, “Priblizhenie analiticheskikh periodicheskikh funktsii lineinymi srednimi ryadov Fure”, Chebyshevskii sb., 17:2 (2016), 170–183  mathnet  elib
    9. Novikov O., Rovenska O., “Approximation of Classes of Poisson Integrals By Repeated Fejer Sums”, Lobachevskii J. Math., 38:3, SI (2017), 502–509  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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