Finiteness of the discrete spectrum of many-particle Hamiltonians in symmetry spaces

Sufficient conditions are found of the finiteness of discrete spectrum of energy operators (in terms of the coordinate and momentum representation) in the symmetry spaces for many-particle systems for which the boundary of continuous spectrum of the Hamiltonian is determined by the dividing into two stable subsystems. In particular, molecules, negative ions of any atoms and systems with short-range interactions are considered. For the systems under consideration the results obtained generalize those known earlier.