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Essential and discrete spectrum of a three-particle lattice Hamiltonian with non-local potentials


We consider a model operator (Hamiltonian) H associated with a system of three particles on a d-dimensional lattice that interact via non-local potentials. Here the kernel of non-local interaction operators has rank n with n ≥ 3. We obtain an analog of the Faddeev equation for the eigenfunctions of H and describe the spectrum of H. It is shown that the essential spectrum of H consists the union of at most n + 1 bounded closed intervals. We estimate the lower bound of the essential spectrum of H for the case d = 1.

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