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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap77-1-7,
author = {Aris Tersenov},
title = {On the solvability of the Lyapunov equation for nonselfadjoint differential operators of order 2m with nonlocal boundary conditions},
journal = {Annales Polonici Mathematici},
volume = {77},
year = {2001},
pages = {79-104},
zbl = {0988.47050},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap77-1-7}
}
Aris Tersenov. On the solvability of the Lyapunov equation for nonselfadjoint differential operators of order 2m with nonlocal boundary conditions. Annales Polonici Mathematici, Tome 77 (2001) pp. 79-104. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap77-1-7/