Duality theory for solutions to Volterra integral equations
type: Item
instance of: scholarly article
title: Duality theory for solutions to Volterra integral equations
zbMATH Open document ID: 0935.45004
author: Michael Jung
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-04-25T00:00:00Z
review text: Consider the equation \[ u(t)=u_0+\int ^t_0 a(t-s)Au(s) ds \] in a Banach space setting. Here \(a\in L^1_{\text{loc}}(R^{+})\), positive for small \(t\), and \(A\) is linear, closed, and densely defined. The author investigates the Favard class of \(A\) and the related sun dual. Results from the duality and sun theory for semigroups are carried over to solution families for Volterra equations. Possible applications to regularity problems for systems of elliptic equations are indicated.
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 1271515
zbMATH Keywords: abstract Volterra equations
zbMATH Keywords: duality theory
zbMATH Keywords: sun theory
zbMATH Keywords: Banach space
reviewed by: Stig-Olof Londen
MaRDI profile type: Publication
full work available at URL: jmaa.1998.6174
OpenAlex ID: W2007244522
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DOI: 10.1006/JMAA.1998.6174
description: scientific article; zbMATH DE number 1271515