1. Threshold phenomenon for a family of the Generalized Generalized Friedrichs models with the perturbation of rank one
- Author
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Lakaev, Saidakhmat N., Darus, Maslina, and Dustov, Said T.
- Subjects
Mathematics - Functional Analysis ,Mathematics - Spectral Theory ,Mathematics - Analysis of PDEs ,FOS: Mathematics ,FOS: Physical sciences ,Mathematical Physics (math-ph) ,Dynamical Systems (math.DS) ,Mathematics - Dynamical Systems ,Spectral Theory (math.SP) ,Mathematical Physics ,Analysis of PDEs (math.AP) ,Functional Analysis (math.FA) ,Forms (bilinear, sesquilinear, multilinear) 47A10 Spectrum, resolvent - Abstract
A family $H_\mu(p),$ $\mu>0,$ $p\in\T^3$ of the Generalized Firedrichs models with the perturbation of rank one, associated to a system of two particles, moving on the three dimensional lattice $\mathbb{\Z}^3,$ is considered. The existence or absence of the unique eigenvalue of the operator $H_\mu(p)$ lying outside the essential spectrum, depending on the values of $\mu>0$ and $p\in U_{\delta}(p_{\,0})\subset\T^3$ is proven. Moreover, the analyticity of associated eigenfunction is shown., Comment: 11 pages
- Published
- 2014
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