Threshold Effects for the Generalized Friedrichs Model with the Perturbation of Rank One

Abstract

A family Hμ(p), μ>0, p∈𝕋2 of the Friedrichs models with the perturbation of rank one, associated to a system of two particles, moving on the two-dimensional lattice ℤ2 is considered. The existence or absence of the unique eigenvalue of the operator Hμ(p) lying below threshold depending on the values of μ>0 and p∈Uδ(0)⊂𝕋2 is proved. The analyticity of corresponding eigenfunction is shown.