  The spectral and scattering properties of non-selfadjoint problems pose a
mathematical challenge. Apart from exceptional cases, the well-developed
methods used to examine the spectrum of selfadjoint problems are not
applicable. One of the tools to attack non-selfadjoint problems are functional
models. A drawback of many functional models is that their constructions
require objects which may be difficult to describe explicitly, such as operator
square roots, making it hard to apply the results to specific examples.
  We develop a functional model for the case when the non-selfadjointness
arises both in additive terms and in the boundary conditions which is based on
the Lagrange identity. The flexibility of the choice of the $\Gamma$-operators
in the Lagrange identity means that these can be chosen so that expressions
arising in the model are given explicitly in terms of physical parameters
(coefficients, boundary conditions and Titchmarsh-Weyl $M$-function) of the
maximally dissipative operator. The presentation of such explicit expressions
for the spectral form of the functional model is arguably the main contribution
of the present paper. In the spectral form of the functional model, the
selfadjoint dilation is very simple, being the operator of multiplication by an
independent variable in some auxiliary vector-valued function space. We also
obtain an explicit expression for the completely non-selfadjoint part of the
operator and an operator-analytic proof of the famous result by Sz.-Nagy-Foias
on the pure absolute continuity of the spectrum of the minimal selfadjoint
dilation. Finally, we consider an example of a limit circle Sturm-Liouville
operator.
