  We discuss the detectable subspaces of an operator. We analyse the relation
between the M-function (the abstract Dirichlet to Neumann map) and the
resolvent bordered by projections onto the detectable subspaces. The abstract
results are explored further by an extensive study of the Friedrichs model,
together with illustrative applications to the Schroedinger and Hain-Luest-type
models.
