Analysis of the spectrum of a 2x2 operator matrix. Discrete spectrum asymptotics
Tulkin H. RasulovFaculty of Physics and Mathematics, Bukhara State University M. Ikbol str. 11, 200100 Bukhara, UzbekistanElyor B. DilmurodovFaculty of Physics and Mathematics, Bukhara State University M. Ikbol str. 11, 200100 Bukhara, Uzbekistan
ABI
Abstract
We consider a 2 2 operator matrix A, > 0 related with the lattice systems describing two identical bosons and one particle, another nature in interactions, without conservation of the number of particles. We obtain an analog of the Faddeev equation and its symmetric version for the eigenfunctions of A. We describe the new branches of the essential spectrum of A via the spectrum of a family of generalized Friedrichs models.
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