  The compression of the resolvent of a non-self-adjoint Schr\"odinger operator
$-\Delta+V$ onto a subdomain $\Omega\subset\mathbb R^n$ is expressed in a
Krein-Naimark type formula, where the Dirichlet realization on $\Omega$, the
Dirichlet-to-Neumann maps, and certain solution operators of closely related
boundary value problems on $\Omega$ and $\mathbb R^n\setminus\overline\Omega$
are being used. In a more abstract operator theory framework this topic is
closely connected and very much inspired by the so-called coupling method that
has been developed for the self-adjoint case by Henk de Snoo and his coauthors.
