  A Gelfand triplet for the Hamiltonian H of the infinite-dimensional
Friedrichs model on the positive half line with Hilbert-Schmidt perturbations
is constructed such that exactly the resonances (poles of the inverse of the
Livsic-matrix) are eigenvalues of the extension H^{\times} of H. The
corresponding eigenantilinear forms are calculated explicitly. Using the wave
matrices for the Abelian wave (M\"oller) operators the corresponding
eigenantilinear forms for the unperturbed Hamiltonian $H_{0}$ turn out to be of
pure Dirac type and can be characterized by their corresponding Gamov vector
which is uniquely determined by restriction to the intersection of the Gelfand
space for $H_{0}$ with $P_{+}H^{2}_{+}$, where $H^{2}_{+}$ is the Hardy space
of the upper half plane. Simultaneously, this restriction yields a truncation
of the unitary evolution $t\to e^{-itH_{0}}$ to the well-known decay semigroup
for $t\geq 0$ of the Toeplitz type on $P_{+}H^{2}_{+}$. That is, exactly those
eigenvectors $\lambda\to k(\lambda-\zeta)^{-1}$, $k$ element of the
multiplicity space K, of the decay semigroup have an extension to an
eigenantilinear form for $H_{0}$ hence for H if $\zeta$ is a resonance and k is
from that subspace of K which is uniquely determined by its corresponding Dirac
type antilinear form. Moreover, the scattering matrix which is meromorphic in
the lower half plane has only simple poles there and the main part of its
Laurent representation is a linear combination of Gamov vectors.
