Matematičeskie zametki, Tome 17 (1975) no. 2, pp. 169-180
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V. A. Baskakov. Some properties of operators of Abel–Poisson type. Matematičeskie zametki, Tome 17 (1975) no. 2, pp. 169-180. http://geodesic.mathdoc.fr/item/MZM_1975_17_2_a0/
@article{MZM_1975_17_2_a0,
author = {V. A. Baskakov},
title = {Some properties of operators of {Abel{\textendash}Poisson} type},
journal = {Matemati\v{c}eskie zametki},
pages = {169--180},
year = {1975},
volume = {17},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_2_a0/}
}
TY - JOUR
AU - V. A. Baskakov
TI - Some properties of operators of Abel–Poisson type
JO - Matematičeskie zametki
PY - 1975
SP - 169
EP - 180
VL - 17
IS - 2
UR - http://geodesic.mathdoc.fr/item/MZM_1975_17_2_a0/
LA - ru
ID - MZM_1975_17_2_a0
ER -
%0 Journal Article
%A V. A. Baskakov
%T Some properties of operators of Abel–Poisson type
%J Matematičeskie zametki
%D 1975
%P 169-180
%V 17
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_1975_17_2_a0/
%G ru
%F MZM_1975_17_2_a0
We obtain asymptotic estimates for approximations of certain classes of continuous and differentiable functions by operators $$ A_{\gamma,r}(f;x)=\frac1\pi\int_{-\pi}^\pi f(x+t)\Bigl(\frac12+\sum_{k=1}^\infty r^{k^\gamma}\operatorname{cor}kt\Bigr)\,dt $$ for $\gamma=1\,\text{and}\,2$.
