  A Gelfand triplet for the Hamiltonian H of the Friedrichs model on R with
finite-dimensional multiplicity space K, is constructed such that exactly the
resonances (poles of the inverse of the Livsic-matrix) are (generalized)
eigenvalues of H. The corresponding eigen-antilinearforms are calculated
explicitly. Using the wave matrices for the wave (Moller) operators the
corresponding eigen-antilinearforms on the Schwartz space S for the unperturbed
Hamiltonian are also calculated. It turns out that they are of pure Dirac type
and can be characterized by their corresponding Gamov vector, which is uniquely
determined by restriction of S to the intersection of S with the Hardy space of
the upper half plane. Simultaneously this restriction yields a truncation of
the generalized evolution to the well-known decay semigroup of the Toeplitz
type for the positive half line on the Hardy space. That is: exactly those
pre-Gamov vectors (eigenvectors of the decay semigroup) have an extension to a
generalized eigenvector of H if the eigenvalue is a resonance and if the
multiplicity parameter k is from that subspace of K which is uniquely
determined by its corresponding Dirac type antilinearform.
