Growth of norms in $L_2$ of derivatives of Steklov functions and properties of functions defined by best approximations and Fourier coefficients
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 31, Tome 445 (2016), pp. 5-32
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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.
@article{ZNSL_2016_445_a0,
author = {M. V. Babushkin and V. V. Zhuk},
title = {Growth of norms in $L_2$ of derivatives of {Steklov} functions and properties of functions defined by best approximations and {Fourier} coefficients},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {5--32},
publisher = {mathdoc},
volume = {445},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_445_a0/}
}
TY - JOUR AU - M. V. Babushkin AU - V. V. Zhuk TI - Growth of norms in $L_2$ of derivatives of Steklov functions and properties of functions defined by best approximations and Fourier coefficients JO - Zapiski Nauchnykh Seminarov POMI PY - 2016 SP - 5 EP - 32 VL - 445 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_2016_445_a0/ LA - ru ID - ZNSL_2016_445_a0 ER -
%0 Journal Article %A M. V. Babushkin %A V. V. Zhuk %T Growth of norms in $L_2$ of derivatives of Steklov functions and properties of functions defined by best approximations and Fourier coefficients %J Zapiski Nauchnykh Seminarov POMI %D 2016 %P 5-32 %V 445 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_2016_445_a0/ %G ru %F ZNSL_2016_445_a0
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. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 31, Tome 445 (2016), pp. 5-32. http://geodesic.mathdoc.fr/item/ZNSL_2016_445_a0/