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 Zap. Nauchn. Sem. POMI, 2016, Volume 445, Pages 5–32 (Mi znsl6274)

Growth of norms in $L_2$ of derivatives of Steklov functions and properties of functions defined by best approximations and Fourier coefficients

M. V. Babushkin, V. V. Zhuk

Saint Petersburg State University, Saint Petersburg, Russia

Abstract: In the paper, for periodic functions, a connection between integrals of norms in $L_2$ of derivatives of Steklov functions and series constructed from Fourier coefficients and the best approximations in $L_2$ is established, and the question on their simultaneous convergence or divergence is considered. Similar investigations are carried out for even and odd periodic functions.

Key words and phrases: Steklov functions, Fourier coefficients, nonnegative Fourier coefficients, best approximation, equiconvergence of series and integrals.

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English version:
Journal of Mathematical Sciences (New York), 2017, 222:5, 525–543

Bibliographic databases:

UDC: 517.5

Citation: M. V. Babushkin, V. V. Zhuk, “Growth of norms in $L_2$ of derivatives of Steklov functions and properties of functions defined by best approximations and Fourier coefficients”, Analytical theory of numbers and theory of functions. Part 31, Zap. Nauchn. Sem. POMI, 445, POMI, St. Petersburg, 2016, 5–32; J. Math. Sci. (N. Y.), 222:5 (2017), 525–543

Citation in format AMSBIB
\Bibitem{BabZhu16} \by M.~V.~Babushkin, V.~V.~Zhuk \paper Growth of norms in $L_2$ of derivatives of Steklov functions and properties of functions defined by best approximations and Fourier coefficients \inbook Analytical theory of numbers and theory of functions. Part~31 \serial Zap. Nauchn. Sem. POMI \yr 2016 \vol 445 \pages 5--32 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl6274} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3511158} \transl \jour J. Math. Sci. (N. Y.) \yr 2017 \vol 222 \issue 5 \pages 525--543 \crossref{https://doi.org/10.1007/s10958-017-3320-9} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85015684243}