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

In the space $L_2(T^ \nu \times T^\nu)$, where $T^\nu$ is a $\nu$-dimensional torus, we study the spectral properties of the "three-particle" discrete Schrödinger operator $\widehat H=H_0+H_1+H_2$, 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 $\widehat H$. We study the discrete and essential spectra of the Hamiltonians $H^{\mathrm{t}}$ and $\mathbf{h}$ arising in the Hubbard model on the three-dimensional lattice.