A representation formula for strongly continuous resolvent families
type: Item
instance of: scholarly article
title: A representation formula for strongly continuous resolvent families
zbMATH Open document ID: 0911.45007
author: Carlos Lizama
published in: Journal of Integral Equations and Applications
publication date: 1999-04-28T00:00:00Z
full work available at URL: cont9-4.htm
review text: The resolvent of the linear Volterra equation \[ u(t)=f(t)+\int_0^ta(t-s)Au(s)ds \] in a Banach space with a closed operator \(A\) is related to \(a\) by a Laplace transform. This relation and a result on the inverse Laplace transform by \textit{B. Hennig} and \textit{F. Neubrander} [Appl. Anal. 49, No. 3-4, 151-170 (1993; Zbl 0791.44002)] leads straightforwardly to an involved formula for the resolvent. From this formula, criteria for a positive resolvent are gained.
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 45M20
zbMATH DE Number: 1185926
zbMATH Keywords: linear Volterra equation in Banach space
zbMATH Keywords: inverse Laplace transform
zbMATH Keywords: Laplace transform
zbMATH Keywords: positive solution
zbMATH Keywords: positive resolvent
MaRDI profile type: Publication
OpenAlex ID: W2066275375
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DOI: 10.1216/JIEA/1181076027
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description: scientific article; zbMATH DE number 1185926