Threshold effects for the generalized Friedrichs model with the perturbation of rank one (Q448607)

Summary: A family \(H_\mu(p), \mu > 0, p \in \mathbb T^2\) of the Friedrichs models with the perturbation of rank one, associated to a system of two particles, moving on the two-dimensional lattice \(\mathbb Z^2\) is considered. The existence or absence of the unique eigenvalue of the operator \(H_\mu(p)\) lying below threshold depending on the values of \(\mu > 0\) and \(p \in U_\delta(0) \subset \mathbb T^2\) is proved. The analyticity of corresponding eigenfunction is shown.