The sharp Jackson inequality in the space $L_2$ on the segment $[-1,1]$ with the power weight
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 3, pp. 112-126
Voir la notice de l'article provenant de la source Math-Net.Ru
In the space $L_2$ on the segment $[-1,1]$ with the power weight $|x|^{2\lambda+1}$, $\lambda\ge-1/2$ , we define a complete orthogonal system, the value of the best approximation with respect to this system, the operator of generalized shift, and the modulus of continuity and prove the sharp Jackson inequality.
@article{TIMM_2008_14_3_a9,
author = {V. I. Ivanov and D. V. Chertova and Liu Yongping},
title = {The sharp {Jackson} inequality in the space $L_2$ on the segment $[-1,1]$ with the power weight},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {112--126},
publisher = {mathdoc},
volume = {14},
number = {3},
year = {2008},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2008_14_3_a9/}
}
TY - JOUR AU - V. I. Ivanov AU - D. V. Chertova AU - Liu Yongping TI - The sharp Jackson inequality in the space $L_2$ on the segment $[-1,1]$ with the power weight JO - Trudy Instituta matematiki i mehaniki PY - 2008 SP - 112 EP - 126 VL - 14 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2008_14_3_a9/ LA - ru ID - TIMM_2008_14_3_a9 ER -
%0 Journal Article %A V. I. Ivanov %A D. V. Chertova %A Liu Yongping %T The sharp Jackson inequality in the space $L_2$ on the segment $[-1,1]$ with the power weight %J Trudy Instituta matematiki i mehaniki %D 2008 %P 112-126 %V 14 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2008_14_3_a9/ %G ru %F TIMM_2008_14_3_a9
V. I. Ivanov; D. V. Chertova; Liu Yongping. The sharp Jackson inequality in the space $L_2$ on the segment $[-1,1]$ with the power weight. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 3, pp. 112-126. http://geodesic.mathdoc.fr/item/TIMM_2008_14_3_a9/