Saturation theorems for families of dual operators
type: Item
instance of: scholarly article
title: Saturation theorems for families of dual operators
zbMATH Open document ID: 0543.41026
DOI: 10.1016/0021-9045(84)90091-1
published in: Journal of Approximation Theory
publication date: 1984-01-01T00:00:00Z
review text: This paper deals with the saturation behaviour of a family of dual operators \(\{\) T'\({}_ t\}\), where \(\{T_ t\}\) is a commutative, strong approximation process on a Banach space X, satisfying a so-called Voronovskaya-type relation. It turns out that the saturation order of \(\{\) T'\({}_ t\}\) is the same as that for \(\{T_ t\}\), and the saturation class of \(\{\) T'\({}_ t\}\) can be characterized in a natural way. Applications are given for semigroups of operators, recovering some results of \textit{K. de Leeuw} [Math. Z. 73, 219-234 (1960; Zbl 0094.105)], and for convolution integrals.
Mathematics Subject Classification ID: 41A40
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A27
Mathematics Subject Classification ID: 41A35
zbMATH DE Number: 3863797
zbMATH Keywords: dual operators
zbMATH Keywords: saturation order
zbMATH Keywords: convolution integrals
author: Sigmar Ries
author: Rudolf L. Stens
MaRDI profile type: Publication
full work available at URL: 0021-9045(84)90091-1
OpenAlex ID: W2080106522
cites work: Interpolationsmethoden zur Behandlung von Approximationsprozessen auf Banachräumen
cites work: Q5549343
cites work: Q5550550
cites work: Q5621638
cites work: Q4751122
cites work: Q5526484
cites work: On the adjoint semigroup and some problems in the theory of approximation
cites work: Q3729517
cites work: Q3249198
cites work: Q5332437
description: scientific article; zbMATH DE number 3863797