Threshold Effects for the Generalized Friedrichs Model with the Perturbation of Rank One. (30th August 2012) - Lakaev, Saidakhmat; Ibrahim, Arsmah; Kurbanov, Shaxzod
Abstract : A family H μ ( p ), μ > 0, p ∈ 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 ℤ 2 is considered. The existence or absence of the unique eigenvalue of the operator H μ ( p ) lying below threshold depending on the values of μ > 0 and p ∈ U δ ( 0 ) ⊂ 𝕋 2 is proved. The analyticity of corresponding eigenfunction is shown.