Subdynamics theory in the functional approach to quantum mechanics

The formalism of subdynamics is extended to the functional approach to quantum systems and is used for the Friedrichs model in which diagonal singularities in states and observables are included. In this approach we compute the generalized eigenvectors and eigenvalues of the Liouville-von Neumann operator, using an iterative scheme. As complex generalized eigenvalues are obtained, the decay rates of unstable modes are included in the spectral decomposition.