A discrete "three-particle" Schrodinger operator in the Hubbard model

In the space L-2 (T-v x T-v), where T-v is a v-dimensional torns, we study the spectral properties of the "three-particle" discrete Shrodinger operator H = H-0 + H-1 + H-2, where H-0 is the operator of multiplication by a function and H-1 and H-2 are partial integral operators. We prove several theorems concerning the essential spectrum of H. We study the discrete and essential spectra of the Hamiltonians H-t and h arising in the Hubbard model on the three-dimensional lattice.