Geodesic
Asymptotics of the discrete spectrum of a model operator associated with a system of three particles on a lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 1, pp. 34-44 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a model Schrödinger operator $H_\mu$ associated with a system of three particles on the three-dimensional lattice $\mathbb Z^3$ with a functional parameter of special form. We prove that if the corresponding Friedrichs model has a zero-energy resonance, then the operator $H_\mu$ has infinitely many negative eigenvalues accumulating at zero (the Efimov effect). We obtain the asymptotic expression for the number of eigenvalues of $H_\mu$ below $z$ as $z\to-0$.
Keywords: model operator, Friedrichs model, Birman–Schwinger principle, Efimov effect, Hilbert–Schmidt operator, zero-energy resonance, discrete spectrum. 
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T. H. Rasulov. Asymptotics of the discrete spectrum of a model operator associated with a system of three particles on a lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 1, pp. 34-44. http://geodesic.mathdoc.fr/item/TMF_2010_163_1_a2/

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