An estimate of an optimal argument in the sharp multidimensional Jackson--Stechkin $L_2$-inequality
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 83-91
Voir la notice de l'article provenant de la source Math-Net.Ru
An estimate of an optimal argument in the sharp Jackson–Stechkin inequality in the space $L_2(\mathbb R^n)$ is proved in the case of a generalized modulus of continuity; its special case is the classical modulus of continuity. Similar statements hold for the torus $\mathbb T^n$. The obtained results agree with Chernykh's classical one-dimensional theorems and refine some results by S. N. Vasil'ev, A. I. Kozko, and N. I. Rozhdestvenskii.
Keywords:
best approximation, generalized modulus of continuity, sharp multidimensional Jackson–Stechkin inequality.
@article{TIMM_2014_20_1_a7,
author = {D. V. Gorbachev},
title = {An estimate of an optimal argument in the sharp multidimensional {Jackson--Stechkin} $L_2$-inequality},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {83--91},
publisher = {mathdoc},
volume = {20},
number = {1},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a7/}
}
TY - JOUR AU - D. V. Gorbachev TI - An estimate of an optimal argument in the sharp multidimensional Jackson--Stechkin $L_2$-inequality JO - Trudy Instituta matematiki i mehaniki PY - 2014 SP - 83 EP - 91 VL - 20 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a7/ LA - ru ID - TIMM_2014_20_1_a7 ER -
%0 Journal Article %A D. V. Gorbachev %T An estimate of an optimal argument in the sharp multidimensional Jackson--Stechkin $L_2$-inequality %J Trudy Instituta matematiki i mehaniki %D 2014 %P 83-91 %V 20 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a7/ %G ru %F TIMM_2014_20_1_a7
D. V. Gorbachev. An estimate of an optimal argument in the sharp multidimensional Jackson--Stechkin $L_2$-inequality. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 83-91. http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a7/