Estimates for the modulus of smoothness
type: Item
instance of: scholarly article
title: Estimates for the modulus of smoothness
zbMATH Open document ID: 0568.41018
DOI: 10.1016/0021-9045(85)90073-5
author: I. G. Graham
published in: Journal of Approximation Theory
publication date: 1985-01-01T00:00:00Z
review text: In approximation theory it is usual for the order of approximation of a function to be given in terms of the modulus of smoothness of that function, but in practice a quantitative estimate of this modulus will be required. In this paper we introduce certain classes of multivariate functions which are characterized by the singularities of their elements. For these classes we obtain sharp quantitative estimates of the modulus of smoothness of any order with respect to both the \(L_ q\) and uniform norms. The aim is to make the theoretical approximation results more accessible to the practical user.
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 41A17
zbMATH DE Number: 3907059
zbMATH Keywords: order of approximation
zbMATH Keywords: modulus of smoothness
zbMATH Keywords: multivariate functions
MaRDI profile type: Publication
full work available at URL: 0021-9045(85)90073-5
OpenAlex ID: W1968294976
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description: scientific article; zbMATH DE number 3907059