  This paper discusses how much information on a Friedrichs model operator can
be detected from `measurements on the boundary'. We use the framework of
boundary triples to introduce the generalised Titchmarsh-Weyl $M$-function and
the detectable subspaces which are associated with the part of the operator
which is `accessible from boundary measurements'. The Friedrichs model, a
finite rank perturbation of the operator of multiplication by the independent
variable, is a toy model that is used frequently in the study of perturbation
problems. We view the Friedrichs model as a key example for the development of
the theory of detectable subspaces, because it is sufficiently simple to allow
a precise description of the structure of the detectable subspace in many
cases, while still exhibiting a variety of behaviours. The results also
demonstrate an interesting interplay between modern complex analysis, such as
the theory of Hankel operators, and operator theory.
