About the sharp Jackson--Nikol'skii inequality for algebraic polynomials on a~multidimensional Euclidean sphere
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 1, pp. 122-134
Voir la notice de l'article provenant de la source Math-Net.Ru
The best constant $C_{nm}$ in the Jackson–Nikol'skii inequality between uniform and integral norms of algebraic polynomials of given total degree $n\ge0$ on the unit sphere $\mathbb S^{m-1}$ of the Euclidean space $\mathbb R^m$ is studied. Two-sided estimates for the constant $C_{nm}$ are obtained, which, in particular, give the order $n^{m-1}$ of its behavior with respect to $n$ as $n\to+\infty$ for a fixed $m$.
Keywords:
multidimensional Euclidean sphere, algebraic polynomials, Jackson–Nikol'skii inequality.
@article{TIMM_2009_15_1_a9,
author = {M. V. Deikalova},
title = {About the sharp {Jackson--Nikol'skii} inequality for algebraic polynomials on a~multidimensional {Euclidean} sphere},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {122--134},
publisher = {mathdoc},
volume = {15},
number = {1},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2009_15_1_a9/}
}
TY - JOUR AU - M. V. Deikalova TI - About the sharp Jackson--Nikol'skii inequality for algebraic polynomials on a~multidimensional Euclidean sphere JO - Trudy Instituta matematiki i mehaniki PY - 2009 SP - 122 EP - 134 VL - 15 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2009_15_1_a9/ LA - ru ID - TIMM_2009_15_1_a9 ER -
%0 Journal Article %A M. V. Deikalova %T About the sharp Jackson--Nikol'skii inequality for algebraic polynomials on a~multidimensional Euclidean sphere %J Trudy Instituta matematiki i mehaniki %D 2009 %P 122-134 %V 15 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2009_15_1_a9/ %G ru %F TIMM_2009_15_1_a9
M. V. Deikalova. About the sharp Jackson--Nikol'skii inequality for algebraic polynomials on a~multidimensional Euclidean sphere. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 1, pp. 122-134. http://geodesic.mathdoc.fr/item/TIMM_2009_15_1_a9/