  In this work we study the Kirkwood-Salsburg equations of equilibrium
classical continuous systems. We prove a Laurent expansion for the resolvent,
at an eigenvalue of largest modulus of the Kirkwood-Salsburg operator, which is
shown to have a pole of order 1. Then we prove that all correlation functions
have an asymptotic limit as the activity parameter tends to a smallest zero of
the partition function. As corollary, we show that any smallest zero of the
partition function is simple. The main consequence is that in case of positive
or hardcore potentials we find the spectral radius of the Kirkwood-Salsburg
operator and the convergence radius of the solutions.
