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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 392, Pages 32–66 (Mi znsl4577)  
This article is cited in 3 scientific papers (total in 3 papers)

Estimates for functionals with a known finite set of moments in terms of deviations of operators constructed with the use of the Steklov averages and finite differences

O. L. Vinogradov, V. V. Zhuk

Saint-Petersburg State University, Saint-Petersburg, Russia
Full-text PDF (369 kB) Citations (3)
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Abstract: The paper presents a new technique for deriving the estimates mentioned in the title. In particular, this technique allows one to establish Jackson-type inequalities for moduli of continuity of arbitrary order with relatively small constants. The results obtained are valid in different spaces of periodic and nonperiodic functions.
Key words and phrases: best approximation, modulus of continuity, sharp constants, Steklov functions.
Received: 12.08.2011
English version:
Journal of Mathematical Sciences (New York), 2012, Volume 184, Issue 6, Pages 679–698
DOI: https://doi.org/10.1007/s10958-012-0890-4
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: O. L. Vinogradov, V. V. Zhuk, “Estimates for functionals with a known finite set of moments in terms of deviations of operators constructed with the use of the Steklov averages and finite differences”, Analytical theory of numbers and theory of functions. Part 26, Zap. Nauchn. Sem. POMI, 392, POMI, St. Petersburg, 2011, 32–66; J. Math. Sci. (N. Y.), 184:6 (2012), 679–698
Citation in format AMSBIB
\Bibitem{VinZhu11}
\by O.~L.~Vinogradov, V.~V.~Zhuk
\paper Estimates for functionals with a~known finite set of moments in terms of deviations of operators constructed with the use of the Steklov averages and finite differences
\inbook Analytical theory of numbers and theory of functions. Part~26
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 392
\pages 32--66
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4577}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2012
\vol 184
\issue 6
\pages 679--698
\crossref{https://doi.org/10.1007/s10958-012-0890-4}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84864283545}
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  • https://www.mathnet.ru/eng/znsl/v392/p32
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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