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
Ochiq kirishBronza
ABI
Annotatsiya
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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