  The correlation function of the product of N generalized vertex operators
satisfies an infinite set of Ward identities, related to a W_{\infty} algebra,
whose extention out of the mass shell gives rise to equations which can be
considered as a generalization of the compactified Calogero-Sutherland (CS)
hamiltonians. In particular the wave function of the ground state of the
compactified CS model is shown to be given by the value of the product of N
vertex operators between the vacuum and exitated state. The role of vertex
algebra as underlying unifying structure is pointed out.
