Geodesic
On the spectrum of a three-particle model operator on a lattice with non-local potentials
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 168-184.

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A model operator $H$ associated to a system of three particles on a ${\rm d}$-dimensional lattice that interact via non-local potentials is considered. The channel operators are identified. An analogue of the Faddeev equation for the eigenfunctions of $H$ is constructed and the spectrum of $H$ is described. The location of the essential spectrum of $H$ is described by the spectrum of channel operators. It is shown that the essential spectrum of $H$ consists the union of at most $2n+1$ bounded closed intervals, where $n$ is the rank of the kernel of non-local interaction operators. The upper bound of the spectrum of $H$ is found. The lower bound of the essential spectrum of $H$ for the case ${\rm d}=1$ is estimated.
Keywords: model operator, discrete Schrödinger operator, non-local interaction operators, Hubbard model, channel operator, Hilbert–Schmidt class, Faddeev equation, essential and discrete spectrum. 
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T. Kh. Rasulov; Z. D. Rasulova. On the spectrum of a three-particle model operator on a lattice with non-local potentials. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 168-184. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a69/

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