Some spectral properties of a generalized Friedrichs model

{We consider self-adjoint generalized Friedrichs model $h(p)$, $p \in {\mathcal T}^3$ (${\mathcal T}^3$ is the three-dimensional torus), in the case where the parameter functions $w_1$ and $w_2$ of this operator has the special forms. These functions has non-degenerate minimum at the several different points. Threshold effects for the considering operator are studied depending on the minimum points of $w_2$.