On the solvability of the Lyapunov equation for nonselfadjoint differential operators of order~\(2m\) with nonlocal boundary conditions
type: Item
instance of: scholarly article
zbMATH Open document ID: 0988.47050
author: A. S. Tersenov
published in: Annales Polonici Mathematici
publication date: 2001-12-11T00:00:00Z
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 47B10
zbMATH DE Number: 1681019
zbMATH Keywords: Lyapunov equation
zbMATH Keywords: compatibility conditions
zbMATH Keywords: nonlocal boundary conditions
zbMATH Keywords: selfadjoint operator
zbMATH Keywords: resolvent
Wikidata QID: Q115218239
MaRDI profile type: Publication
full work available at URL: ap77-1-7
OpenAlex ID: W2072160125
DOI: 10.4064/AP77-1-7
title: On the solvability of the Lyapunov equation for nonselfadjoint differential operators of order~\(2m\) with nonlocal boundary conditions
review text: Let \(A\) be a selfadjoint operator of order \(2m\) with nonlocal boundary conditions in spaces of vector-valued functions of one independent variable and let \(A^*\) be its adjoint. We assume that the spectra of the operators \(A^*\) and \(-A\) are disjoint and for some real \(\beta\) and \(\theta\) \((\pi/2<\theta<\pi)\) the resolvent \(R(A,\lambda)\) of \(A\) is uniformly bounded with respect to \(\lambda\) in the sector \(|\text{arg}(\lambda-\beta)|\leq \theta\). Under these assumptions the author investigates the solvability of the Lyapunov equation \(A^*U+UA=I\), where \(I\) is the identity operator and \(U\) denotes a selfadjoint operator to be found.
reviewed by: Józef Banaś
description: scientific article; zbMATH DE number 1681019