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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 429, Pages 20–33 (Mi znsl6064)  
On approximation of periodic functions by modified Steklov averages in $L_2$

V. O. Dron, V. V. Zhuk

St. Petersburg State University, St. Petersburg, Russia
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Abstract: In the space $L_2$ of periodic functions, sharp (in the sence of constants) estimates from below for the deviation of the modified Steklov functions of the first and second order in terms of the modulus of continuity are established. Similar results are also obtained for even continuous periodic functions with nonnegative Fourier coefficients in the space $C$.
Key words and phrases: the $L_2$ space, modifications of Steklov averages, exact constants, moduli of continuity, Fourier series with positive coefficients.
Received: 02.09.2014
English version:
Journal of Mathematical Sciences (New York), 2015, Volume 207, Issue 6, Pages 815–824
DOI: https://doi.org/10.1007/s10958-015-2405-6
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: V. O. Dron, V. V. Zhuk, “On approximation of periodic functions by modified Steklov averages in $L_2$”, Analytical theory of numbers and theory of functions. Part 29, Zap. Nauchn. Sem. POMI, 429, POMI, St. Petersburg, 2014, 20–33; J. Math. Sci. (N. Y.), 207:6 (2015), 815–824
Citation in format AMSBIB
\Bibitem{DroZhu14}
\by V.~O.~Dron, V.~V.~Zhuk
\paper On approximation of periodic functions by modified Steklov averages in~$L_2$
\inbook Analytical theory of numbers and theory of functions. Part~29
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 429
\pages 20--33
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6064}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 207
\issue 6
\pages 815--824
\crossref{https://doi.org/10.1007/s10958-015-2405-6}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84949626657}
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