Rational approximation schemes for bi-continuous semigroups
type: Item
instance of: scholarly article
title: Rational approximation schemes for bi-continuous semigroups
zbMATH Open document ID: 1153.47027
author: Patricio Jara
published in: Journal of Mathematical Analysis and Applications
publication date: 2008-06-17T00:00:00Z
review text: An operator semigroup \(T(t)_{t\geq 0}\) on a Banach space \(X\) is said to be of type \((M,\omega)\) if, for some \(M> 1\) and \(\omega\in\mathbb{R}\), one has that \(\| T(t)\|\leq Me^{\omega t}\) for all \(t\geq 0\). Such a semigroup is called bi-continuous with respect to some topology \(\tau\) coherent with the norm topology on \(X\) if it is strongly \(\tau\)-continuous and also has a certain bi-equicontinuity property. In this paper, the author constructs the Hille--Phillips functional calculus (defined in terms of Laplace--Stieltjes integrals) for generators of bi-continuous semigroups. Some rational approximation results known for strongly continuous semigroups are also extended to bi-continuous semigroups. The results provide error estimates for a new class of inversion formulas for the Laplace transform.
Mathematics Subject Classification ID: 47D03
zbMATH DE Number: 5289201
zbMATH Keywords: bicontinuous semigroups
zbMATH Keywords: Hille-Phillips functional calculus
zbMATH Keywords: Laplace transform inversion
zbMATH Keywords: time-discretisation
reviewed by: Khristo N. Boyadzhiev
describes a project that uses: RODAS
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.02.068
OpenAlex ID: W1964215832
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DOI: 10.1016/J.JMAA.2008.02.068
description: scientific article; zbMATH DE number 5289201