Geodesic
Essential spectrum of a~model operator associated with a~three-particle system on a~lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 166 (2011) no. 1, pp. 95-109

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We consider a model operator $H$ associated with the system of three particles interacting via nonlocal pair potentials on a $\nu$-dimensional lattice. We identify channel operators and use their spectra to describe the position and structure of the essential spectrum of $H$. We obtain an analogue of the Faddeev equation for the eigenfunctions of $H$.
Keywords: model operator, nonlocal potential, Hilbert–Schmidt class, Faddeev equation, essential spectrum, channel operator. 
@article{TMF_2011_166_1_a6,
     author = {T. H. Rasulov},
     title = {Essential spectrum of a~model operator associated with a~three-particle system on a~lattice},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {95--109},
     publisher = {mathdoc},
     volume = {166},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_166_1_a6/}
}
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T. H. Rasulov. Essential spectrum of a~model operator associated with a~three-particle system on a~lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 166 (2011) no. 1, pp. 95-109. http://geodesic.mathdoc.fr/item/TMF_2011_166_1_a6/