@article{Rasulov_Dilmurodov_2020, title={Estimates for the Bounds of the Essential Spectrum of a 2 × 2 Operator Matrix}, volume={1}, url={http://ojs.wiserpub.com/index.php/CM/article/view/409}, DOI={10.37256/cm.142020409}, abstractNote={<p>We consider a 2 × 2 operator matrix <em>Aμ, μ </em>> 0, related with the lattice systems describing three particles in interaction, without conservation of the number of particles on a d-dimensional lattice. We obtain an analogue of the Faddeev type integral equation for the eigenfunctions of <em>Aμ</em>. We describe the two- and three-particle branches of the essential spectrum of <em>Aμ </em>via the spectrum of a family of generalized Friedrichs models. It is shown that the essential spectrum of <em>Aμ </em>consists of the union of at most three bounded closed intervals. We estimate the lower and upper bounds of the essential spectrum of <em>Aμ </em>with respect to the dimension d ∈ N of the torus T<sup>d</sup> and the coupling constant <em>μ </em>> 0.</p>}, number={4}, journal={Contemporary Mathematics}, author={Rasulov, Tulkin and Dilmurodov, Elyor B.}, year={2020}, month={Jul.} }