C-admissibility and analytic \(C\)-semigroups
type: Item
instance of: scholarly article
title: C-admissibility and analytic \(C\)-semigroups
zbMATH Open document ID: 1236.47041
author: Saud M. Alsulami
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2011-07-22T00:00:00Z
review text: This paper gives a uniqueness result for the solution of the operator equation \(AX-XB=CD\) in the case of \(A\) being the generator of an analytic \(C\)-regularized semigroup in a Banach space \(F\) and \(B\) being a closed linear operator in \(F\) with some further properties. When \(C=I\), the result was proved by \textit{Q. P. Vu} and \textit{E. Schüler} in [J. Differ. Equations 145, No. 2, 394--419 (1998; Zbl 0918.34059)].
reviewed by: Jin Liang
Mathematics Subject Classification ID: 47D60
zbMATH DE Number: 5930968
zbMATH Keywords: operator equation
zbMATH Keywords: analytic \(C\)-regularized semigroups
zbMATH Keywords: uniqueness
MaRDI profile type: Publication
full work available at URL: j.na.2011.05.066
OpenAlex ID: W1507588615
cites work: The operator equation \(AX-XB=C\), admissibility, and asymptotic behavior of differential equations
cites work: The operator equation \(AX-XB=C\) with unbounded operators \(A\) and \(B\) and related abstract Cauchy problems
cites work: A remark on exponentially bounded C-semigroups
cites work: \(C\)-semigroups and strongly continuous semigroups
cites work: Holomorphic C-semigroups and holomorphic semigroups
DOI: 10.1016/J.NA.2011.05.066
description: scientific article; zbMATH DE number 5930968