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Zap. Nauchn. Sem. POMI, 2011, Volume 392, Pages 32–66 (Mi znsl4577)  

This article is cited in 2 scientific papers (total in 2 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

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.

Full text: PDF file (369 kB)
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English version:
Journal of Mathematical Sciences (New York), 2012, 184:6, 679–698

UDC: 517.5
Received: 12.08.2011

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Zhuk, “Inequalities of type generalized Jackson theorem for best approximations”, J. Math. Sci. (N. Y.), 193:1 (2013), 75–88  mathnet  crossref  mathscinet
    2. O. L. Vinogradov, V. V. Zhuk, “Estimates for functionals with a known finite set of moments in terms of high order moduli of continuity in the spaces of functions defined on the segment”, St. Petersburg Math. J., 25:3 (2014), 421–446  mathnet  crossref  mathscinet  zmath  isi  elib
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