On the sharp Jackson-Nikol'skii inequality for algebraic polynomials on a multidimensional Euclidean sphere
type: Item
instance of: scholarly article
title: On the sharp Jackson-Nikol'skii inequality for algebraic polynomials on a multidimensional Euclidean sphere
zbMATH Open document ID: 1229.41014
DOI: 10.1134/S0081543809060108
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2011-11-02T00:00:00Z
review text: Jackson-Nikol'skii inequalities and their constants are considered in this article for different dimensions \(m\) and polynomial degrees \(n\). Here, \(n\) is the total degree of a polynomial in \(m\) variables. Uniform and \(L^1\)-norms of such polynomials are compared by these estimates, and the central question is the dependence of the best possible constants in the inequalities on \(m\) and \(n\). These are estimated from above and below by multiples of \(n^{m-1}\).
reviewed by: Martin D. Buhmann
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 5966562
zbMATH Keywords: multidimensional Euclidean sphere
zbMATH Keywords: algebraic polynomials
zbMATH Keywords: Jackson-Nikol'skii inequality
author: Marina Valer'evna Deikalova
MaRDI profile type: Publication
cites work: Certain problems of closest approximation
description: scientific article; zbMATH DE number 5966562