  We consider radial complex scaling/perfectly matched layer methods for scalar
resonance problems in homogeneous exterior domains. We introduce a new abstract
framework to analyze the convergence of domain truncations and discretizations.
Our theory requires rather minimal assumptions on the scaling profile and
includes affin, smooth and also unbounded profiles. We report a swift technique
to analyze the convergence of domain truncations and a more technical one for
approximations through simultaneaous truncation and discretization. We adapt
the latter technique to cover also so-called exact methods which do not require
a domain truncation. Our established results include convergence rates of
eigenvalues and eigenfunctions.
  The introduced framework is based on the ideas to interpret the domain
truncation as Galerkin approximation, to apply theory on holomorphic Fredholm
operator eigenvalue approximation theory to a linear eigenvalue problem, to
employ the notion of weak T-coercivity and T-compatible approximations, to
construct a suitable T-operator as multiplicatin operator, to smooth its symbol
and to apply the discrete commutator technique.

Numerical Analysis;Numerical Analysis