Puiseux series expansion for an eigenvalue of the generalized Friedrichs model with perturbation of rank 1

A family Hμ(p), μ > 0, p element of T of the generalized Friedrichs model with perturbation of rank 1, associated with a system of two particles, moving on the one-dimensional lattice Z is considered. The existence of a unique eigenvalue E(μ, p), of the operator Hμ(p) lying below the essential spectrum is proved. For any p from a neighborhood of the origin, the Puiseux series expansion for eigenvalue E(μ, p) at the point μ = μ(p) ⩾ 0 is found. Moreover, the asymptotics for E(μ, p) is established as μ → +∞. (paper)