Geodesic
On the order of approximation of a~continuous $2\pi$-periodic function by Fejer and Poisson means of its Fourier series
Matematičeskie zametki, Tome 4 (1968) no. 1, pp. 21-32

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\sigma_n(f)$ and $P_r(f)$ be, respectively, the Fejer and Poisson means of the Fourier series of the function $f$. The present work considers problems associated with the rapidity of approximation of a continuous $2\pi$-periodic function by means of Fejer and Poisson processes, and gives, in particular, an upper bound to the deviation of the Fejer and Poisson processes from the function in terms of moduli of continuity, and a lower bound to $\|\sigma_n(f)-f\|$ in terms of functionals composed of best approximations to the function $f$; in addition, some relationships among the quantities $\|P_r(f)-f\|$ and $\|\sigma_n(f)-f\|$ are established. 
@article{MZM_1968_4_1_a2,
     author = {V. V. Zhuk},
     title = {On the order of approximation of a~continuous $2\pi$-periodic function by {Fejer} and {Poisson} means of its {Fourier} series},
     journal = {Matemati\v{c}eskie zametki},
     pages = {21--32},
     publisher = {mathdoc},
     volume = {4},
     number = {1},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_1_a2/}
}
TY  - JOUR
AU  - V. V. Zhuk
TI  - On the order of approximation of a~continuous $2\pi$-periodic function by Fejer and Poisson means of its Fourier series
JO  - Matematičeskie zametki
PY  - 1968
SP  - 21
EP  - 32
VL  - 4
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1968_4_1_a2/
LA  - ru
ID  - MZM_1968_4_1_a2
ER  - 
%0 Journal Article
%A V. V. Zhuk
%T On the order of approximation of a~continuous $2\pi$-periodic function by Fejer and Poisson means of its Fourier series
%J Matematičeskie zametki
%D 1968
%P 21-32
%V 4
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1968_4_1_a2/
%G ru
%F MZM_1968_4_1_a2
V. V. Zhuk. On the order of approximation of a~continuous $2\pi$-periodic function by Fejer and Poisson means of its Fourier series. Matematičeskie zametki, Tome 4 (1968) no. 1, pp. 21-32. http://geodesic.mathdoc.fr/item/MZM_1968_4_1_a2/