The Essential Spectrum of a Three Particle Schrodinger Operator on Lattices

We consider the Hamiltonian H-mu lambda, mu, lambda is an element of R of a system of three-particles (two identical bosons and one different particle) moving on the lattice Zd, d = 1, 2 interacting through zero-range pairwise potentials mu not equal 0 and lambda not equal 0. The essential spectrum of the three-particle discrete Schrodinger operator H-mu lambda(K), K is an element of T-d, being the three-particle quasi-momentum, is described by means of the spectrumof non-perturbed three-particle operator H-0(K) and the two-particle discrete Schrodinger operator h(mu)(k), h(lambda,gamma)(k), k is an element of T-d, gamma > 0. It is established that the essential spectrum of the three-particle discrete Schrodinger operator H-mu lambda(K), K is an element of T-d consists of no more than three bounded closed intervals.