Geodesic
On the solvability of the Lyapunov equation for nonselfadjoint differential operators of order $2m$ with nonlocal boundary conditions
Aris Tersenov1
1 Institute of Applied and Computing Mathematics FO.R.T.H. Heraklion, Crete 71110, Greece
Annales Polonici Mathematici, Tome 77 (2001) no. 1, pp. 79-104 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ap77-1-7
Keywords: paper devoted solvability lyapunov equation *u where given nonselfadjoint differential operator order nonlocal boundary conditions * its adjoint identity operator selfadjoint operator found assume spectra * a disjoint under restriction prove existence uniqueness solution lyapunov equation class bounded operators

Aris Tersenov 1

1 Institute of Applied and Computing Mathematics FO.R.T.H. Heraklion, Crete 71110, Greece 
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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) no. 1, pp. 79-104. doi: 10.4064/ap77-1-7

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