Geodesic
On the essential spectrum of a~model operator associated with the system of three particles on a~lattice
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2011), pp. 42-51

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A model operator $H$ associated with the system of three-identical particles on a lattice $\mathbb{Z}^3$ is considered. The location of the essential spectrum of $H$ is described by the spectrum of the corresponding Friedrichs model, that is, the two-particle and three-particle branches of the essential spectrum of $H$ are singled out. It is proved that the essential spectrum of $H$ consists of no more than three bounded closed intervals. An appearance of two-particle branches on the both sides of the three-particle branch is shown. Moreover, we obtain an analogue of the Faddeev equation and its symmetric version, for the eigenfunctions of $H.$
Keywords: model operator, Friedrichs model, Hilbert–Schmidt class, Faddeev equation, essential spectrum. 
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     author = {T. Kh. Rasulov},
     title = {On the essential spectrum of a~model operator associated with the system of three particles on a~lattice},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {42--51},
     publisher = {mathdoc},
     number = {3},
     year = {2011},
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     url = {http://geodesic.mathdoc.fr/item/VSGTU_2011_3_a3/}
}
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T. Kh. Rasulov. On the essential spectrum of a~model operator associated with the system of three particles on a~lattice. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2011), pp. 42-51. http://geodesic.mathdoc.fr/item/VSGTU_2011_3_a3/