Matematičeskie zametki, Tome 9 (1971) no. 6, pp. 617-627
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V. A. Baskakov. The order of approximation of continuous functions by certain linear means of their Fourier series. Matematičeskie zametki, Tome 9 (1971) no. 6, pp. 617-627. http://geodesic.mathdoc.fr/item/MZM_1971_9_6_a1/
@article{MZM_1971_9_6_a1,
author = {V. A. Baskakov},
title = {The order of approximation of continuous functions by certain linear means of their {Fourier} series},
journal = {Matemati\v{c}eskie zametki},
pages = {617--627},
year = {1971},
volume = {9},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1971_9_6_a1/}
}
TY - JOUR
AU - V. A. Baskakov
TI - The order of approximation of continuous functions by certain linear means of their Fourier series
JO - Matematičeskie zametki
PY - 1971
SP - 617
EP - 627
VL - 9
IS - 6
UR - http://geodesic.mathdoc.fr/item/MZM_1971_9_6_a1/
LA - ru
ID - MZM_1971_9_6_a1
ER -
%0 Journal Article
%A V. A. Baskakov
%T The order of approximation of continuous functions by certain linear means of their Fourier series
%J Matematičeskie zametki
%D 1971
%P 617-627
%V 9
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_1971_9_6_a1/
%G ru
%F MZM_1971_9_6_a1
The exact order of the quantity $$A_n(\mathfrak M)=\sup_{\Lambda\in\Lambda^*}\sup_{f\in\mathfrak M}\max_x|L_n(f;x;\Lambda)-f(x)|$$ is determined, where $\Lambda^*$ is the class of linear methods of summation of Fourier series $L_n(f;x;\Lambda)$, satisfying $$(n+1)^{p-1}\sum_{k=0}^n|\Delta\lambda_k^{(n)}|^p\leqslant K^*,\quad p>1$$ and $\mathfrak M$ is either the set of continuous functions $H(\omega)$ or $C(F)$. In
