Structural operators and eigenmanifold decomposition for functional differential equations in Hilbert spaces
type: Item
instance of: scholarly article
title: Structural operators and eigenmanifold decomposition for functional differential equations in Hilbert spaces
zbMATH Open document ID: 0906.47033
author: Shin-Ichi Nakagiri
author: Hiroki Tanabe
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-11-22T00:00:00Z
review text: The authors study spectral properties of linear retarded functional differential equations \[ {du(t)\over dt}= A_0u(t)+ A_1u(t- h)+ \int^0_{-h} a(s)A_2u(t+ s)ds+ f(t)\quad\text{a.e. }t\geq 0, \] \[ u(0)= g^0,\quad u(s)= g^1(s)\quad\text{a.e. }s\in [-h, 0), \] and its transposed equation \[ {dv(t)\over dt}= A^*_0v(t)+ A^*_1 v(t- h)+ \int^0_{-h} a(s) A^*_2v(t+ s)ds+ h(t)\quad\text{a.e. }t\geq 0, \] \[ v(0)= \varphi^0,\quad v(s)= \varphi^1(s)\quad\text{a.e. }s\in [-h,0), \] in Hilbert spaces with the emphasis on their relations to structural operators. The results extend those by \textit{S. Nakagiri} [Osaka J. Math. 25, No. 2, 353-398 (1988; Zbl 0713.34069)] to the above equations considered by \textit{J.-M. Jeong}, \textit{S. Nakagiri} and \textit{H. Tanabe} [Osaka J. Math. 30, No. 3, 365-395 (1993; Zbl 0818.47039)].
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 47D09
zbMATH DE Number: 1005653
zbMATH Keywords: structural operator
zbMATH Keywords: infinitesimal generator
zbMATH Keywords: semigroup
zbMATH Keywords: spectral properties
zbMATH Keywords: linear retarded functional differential equations
zbMATH Keywords: transposed equation
reviewed by: Svatoslav Staněk
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0454
OpenAlex ID: W1964434300
DOI: 10.1006/JMAA.1996.0454
description: scientific article; zbMATH DE number 1005653