  We describe a new form of diagonalization for linear two point constant
coefficient differential operators with arbitrary linear boundary conditions.
Although the diagonalization is in a weaker sense than that usually employed to
solve initial boundary value problems (IBVP), we show that it is sufficient to
solve IBVP whose spatial parts are described by such operators. We argue that
the method described may be viewed as a reimplementation of the Fokas transform
method for linear evolution equations on the finite interval. The results are
extended to multipoint and interface operators, including operators defined on
networks of finite intervals, in which the coefficients of the differential
operator may vary between subintervals, and arbitrary interface and boundary
conditions may be imposed; differential operators with piecewise constant
coefficient are thus included. Both homogeneous and inhomogeneous problems are
solved.
