Matematičeskie zametki, Tome 4 (1968) no. 3, pp. 291-300
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S. A. Telyakovskii. Approximation of differentiable functions by partial sums of their Fourier series. Matematičeskie zametki, Tome 4 (1968) no. 3, pp. 291-300. http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a4/
@article{MZM_1968_4_3_a4,
author = {S. A. Telyakovskii},
title = {Approximation of differentiable functions by partial sums of their {Fourier} series},
journal = {Matemati\v{c}eskie zametki},
pages = {291--300},
year = {1968},
volume = {4},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a4/}
}
TY - JOUR
AU - S. A. Telyakovskii
TI - Approximation of differentiable functions by partial sums of their Fourier series
JO - Matematičeskie zametki
PY - 1968
SP - 291
EP - 300
VL - 4
IS - 3
UR - http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a4/
LA - ru
ID - MZM_1968_4_3_a4
ER -
%0 Journal Article
%A S. A. Telyakovskii
%T Approximation of differentiable functions by partial sums of their Fourier series
%J Matematičeskie zametki
%D 1968
%P 291-300
%V 4
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a4/
%G ru
%F MZM_1968_4_3_a4
For the classes of differentiable functions $W_\alpha^r$, $r>0$, which include the classes of functions which have derivatives $f^{(r)}$ or $\tilde{f}^{(r)}$ with moduli bounded by one, we obtain an asymptotic formula for the supremum of the difference between a function and the partial sums of its Fourier series. The remainder term in our formula is $Cn^{-r}$, in which $C$ is a constant.
