Faddeev equation and its symmetric version for a three-particle lattice hamiltonian

In the present paper we consider the three-particle lattice Hamiltonian associated to a system of three particles on the d-dimensional lattice, where the role of two-particle discrete Schroedinger operators is played by a family of Friedrichs models. We define two bounded and self-adjoint so-called channel operators and prove that the essential spectrum of considered Hamiltonian is the union of spectra of the channel operators. Since the channel operators have a more simple structure than considered Hamiltonian, this fact plays an important role in the subsequent investigations of the essential spectrum. The spectrum of the constructed channel operators are described by the spectrum of the corresponding Friedrichs model. The Faddeev equation and its symmetric version for the eigenfunctions of the considered Hamiltonian are constructed.