On the essential spectrum of a model operator associated with the system of three particles on a lattice

A model operator H associated with the system of three-identical particles on a lattice ℤ3 is considered. The location of the essential spectrum of H is described by the spectrum of the corresponding Friedrichs model, that is, the two-particle and three-particle branches of the essential spectrum of H are singled out. It is proved that the essential spectrum of H consists of no more than three bounded closed intervals. An appearance of two-particle branches on the both sides of the three-particle branch is shown. Moreover, we obtain an analogue of the Faddeev equation and its symmetric version, for the eigenfunctions of H.