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

### Tom 77 / 2001

Annales Polonici Mathematici 77 (2001), 79-104 MSC: 34G10, 34B05, 47E05, 47N20. DOI: 10.4064/ap77-1-7

#### Streszczenie

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.

#### Autorzy

• Aris TersenovInstitute of Applied and Computing Mathematics
FO.R.T.H. Heraklion, Crete 71110, Greece
e-mail

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