Some spectral properties of a generalized Friedrichs model

Abstract

We consider self-adjoint generalized Friedrichs model h(p), p ∈ T3 (T3 is the threedimensional torus), in the case where the parameter functions w1 and w2 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 w2.

Keywords

• generalized friedrichs model
• zero energy resonance
• eigenvalue
• fredholm determinant