Essential self-adjointness of the elliptic Ruijsenaars models

We study the elliptic Ruijsenaars models associated with arbitrary root sys tems, which are difference analogs of the Calogero-Moser model. We give a d ense subspace in the space of square integrable functions invariant under t he action of the Weyl group on a torus as a domain of its Hamiltonian and p rove its essential self-adjointness by using perturbation theory. It is als o clarified that these models consist of pure point spectrum. (C) 2001 Amer ican Institute of Physics.