Puiseux series expansion for an eigenvalue of the generalized Friedrichs model with perturbation of rank 1
S. N. LakaevDepartment of Mathematics, Samarkand State University, Samarkand, UzbekistanMaslina DarusSchool of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan, MalaysiaShaxzod KurbanovDepartment of Mathematics, Samarkand State University, Samarkand, Uzbekistan
ABI
Abstract
A family Hμ(p), μ > 0, of the generalized Friedrichs model with perturbation of rank 1, associated with a system of two particles, moving on the one-dimensional lattice 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 → +∞.
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