Series expansions and small solutions for Volterra equations of convolution type
type: Item
instance of: scholarly article
title: Series expansions and small solutions for Volterra equations of convolution type
zbMATH Open document ID: 0708.34063
DOI: 10.1016/0022-0396(90)90087-6
author: Sjoerd M. Verduyn Lunel
published in: Journal of Differential Equations
publication date: 1990-01-01T00:00:00Z
review text: Necessary conditions for representability of the solutions of Volterra equations of convolution type \(x-\zeta *x=f,p\) where \(\zeta\) is an \(n\times n\)-matrix-valued function on [0,h] of bounded variation, as a series of characteristic solutions, are given. The geometric properties of the strongly continuous semigroup T(t) associated with this equation are investigated, especially, the closure of the linear hull of the system of generalized eigenfunctions of the infinitesimal generator of the semigroup T(t) is considered. Finally, it is shown the existence of a closed minimal invariant subspace of the phase space, carrying all information on the equation.
Mathematics Subject Classification ID: 34K05
zbMATH DE Number: 4163326
zbMATH Keywords: semigroup of operators
zbMATH Keywords: Volterra equations of convolution type
zbMATH Keywords: phase space
reviewed by: R. R. Akhmerov
MaRDI profile type: Publication
full work available at URL: 0022-0396(90)90087-6
OpenAlex ID: W2122377858
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description: scientific article; zbMATH DE number 4163326