Preprint 21-2005

On locally definitizable matrix functions

Author(s) : Tomas Azizov , Peter Jonas

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 21-2005

MSC 2000

47A56 Functions whose values are linear operators

47B50 Operators on spaces with an indefinite metric

Abstract :
For a domain $\Omega$ of the extended complex plane, classes of R-symmetric piecewise meromorphic matrix functions $G$ in $\Omega \setminus \overline{R}$ are studied. If $G$ is locally definitizable in $\Omega$ or a local generalized Nevanlinna function in $\Omega$, then the same is true for the inverse of $G$. The results are applied to an abstract boundary value problem with eigenvalue parameter in the boundary condition.

Keywords : generalized Nevanlinna matrix functions, definitizable matrix functions, locally definitizable matrix functions, selfadjoint operators in Krein spaces, locally definitizable operators