  A general formalism is worked out for the description of one-dimensional
scattering in non-hermitian quantum mechanics and constraints on transmission
and reflection coefficients are derived in the cases of P, T, or PT invariance
of the Hamiltonian. Applications to some solvable PT-symmetric potentials are
shown in detail. Our main original results concern the association of
reflectionless potentials with asymptotic exact PT symmetry and the
peculiarities of separable kernels of non-local potentials in connection with
hermiticity, T invariance and PT invariance.
