On the solvability of the Lyapunov equation for nonselfadjoint differential operators of order 2m with nonlocal boundary conditions

Aris Tersenov. "On the solvability of the Lyapunov equation for nonselfadjoint differential operators of order 2m with nonlocal boundary conditions." Annales Polonici Mathematici 77.1 (2001): 79-104. <http://eudml.org/doc/281057>.

@article{ArisTersenov2001,
abstract = {This paper is devoted to the solvability of the Lyapunov equation A*U + UA = I, where A is a given nonselfadjoint differential operator of order 2m with nonlocal boundary conditions, A* is its adjoint, I is the identity operator and U is the selfadjoint operator to be found. We assume that the spectra of A* and -A are disjoint. Under this restriction we prove the existence and uniqueness of the solution of the Lyapunov equation in the class of bounded operators.},
author = {Aris Tersenov},
journal = {Annales Polonici Mathematici},
keywords = {Lyapunov equation; compatibility conditions; nonlocal boundary conditions; selfadjoint operator; resolvent},
language = {eng},
number = {1},
pages = {79-104},
title = {On the solvability of the Lyapunov equation for nonselfadjoint differential operators of order 2m with nonlocal boundary conditions},
url = {http://eudml.org/doc/281057},
volume = {77},
year = {2001},
}

TY - JOUR
AU - Aris Tersenov
TI - On the solvability of the Lyapunov equation for nonselfadjoint differential operators of order 2m with nonlocal boundary conditions
JO - Annales Polonici Mathematici
PY - 2001
VL - 77
IS - 1
SP - 79
EP - 104
AB - This paper is devoted to the solvability of the Lyapunov equation A*U + UA = I, where A is a given nonselfadjoint differential operator of order 2m with nonlocal boundary conditions, A* is its adjoint, I is the identity operator and U is the selfadjoint operator to be found. We assume that the spectra of A* and -A are disjoint. Under this restriction we prove the existence and uniqueness of the solution of the Lyapunov equation in the class of bounded operators.
LA - eng
KW - Lyapunov equation; compatibility conditions; nonlocal boundary conditions; selfadjoint operator; resolvent
UR - http://eudml.org/doc/281057
ER -