Matematičeskie zametki, Tome 3 (1968) no. 5, pp. 587-596
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S. Z. Rafal'son. Mean approximation of functions by Fourier-Gegenbauer sums. Matematičeskie zametki, Tome 3 (1968) no. 5, pp. 587-596. http://geodesic.mathdoc.fr/item/MZM_1968_3_5_a11/
@article{MZM_1968_3_5_a11,
author = {S. Z. Rafal'son},
title = {Mean approximation of functions by {Fourier-Gegenbauer} sums},
journal = {Matemati\v{c}eskie zametki},
pages = {587--596},
year = {1968},
volume = {3},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1968_3_5_a11/}
}
TY - JOUR
AU - S. Z. Rafal'son
TI - Mean approximation of functions by Fourier-Gegenbauer sums
JO - Matematičeskie zametki
PY - 1968
SP - 587
EP - 596
VL - 3
IS - 5
UR - http://geodesic.mathdoc.fr/item/MZM_1968_3_5_a11/
LA - ru
ID - MZM_1968_3_5_a11
ER -
%0 Journal Article
%A S. Z. Rafal'son
%T Mean approximation of functions by Fourier-Gegenbauer sums
%J Matematičeskie zametki
%D 1968
%P 587-596
%V 3
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1968_3_5_a11/
%G ru
%F MZM_1968_3_5_a11
Necessary and sufficient conditions for best approximations of functions in the $L^2_{(1-x^2)^\alpha}(-1,1)$ metric, $-1/2\le\alpha<1/2$ to zero at a certain rate are established (for $\alpha=?1/2$ known results are obtained). Inequalities for algebraic polynomials are used in the reasoning.
