Threshold Effects for the Generalized Friedrichs Model with the Perturbation of Rank One. (30th August 2012)

• Record Type: Journal Article
• Authors: Lakaev, Saidakhmat; Ibrahim, Arsmah; Kurbanov, Shaxzod
• Other Names: Bertsch Michiel Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-08-30
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/180953
• Languages: English
• ISSNs: 1085-3375

Abstract

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.