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

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Tersenov A.

Annales Polonici Mathematici

2001

tom 77

nr 1

79-104

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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Tersenov A.

1 2001

Wyniki wyszukiwania

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