Derivation of factorization properties for highly connected N-body equations

Resorting to cluster expansions for the full N-body resolvent, we show that highly-connected-kernel equations, can be obtained by multiplying two-body connected-kernel equations, having only physical solutions, by an appropriate multiplier, which can introduce spurious homogeneous solutions. It is also explicitly shown that the factorization property for the four-body Rosenberg-like equations is the four-body analogue (matrix version) of the factorization property for the three-body Weinberg-Van Winter equation.