Discrete Spectrum of a Model Operator Related to Three-Particle Discrete Schrödinger Operators

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dc.creatorRasulov, Tulkin H.
dc.date2009-04-14
dc.date2009-04-27
dc.date.accessioned2026-07-07T13:08:22Z
dc.date.available2026-07-07T13:08:22Z
dc.descriptionA model operator $H_μ,$ $μ>0$ associated to a system of three particles on the three-dimensional lattice $ \mathbb{Z}^3$ that interact via nonlocal pair potentials is considered. We study the case where the parameter function $w$ has a special form with the non degenerate minimum at the $n, n>1$ points of the six-dimensional torus $\mathbb{T}^6.$ If the associated Friedrichs model has a zero energy resonance, then we prove that the operator $H_μ$ has infinitely many negative eigenvalues accumulating at zero and we obtain an asymptotics for the number of eigenvalues of $H_μ$ lying below $z,$ $z<0$ as $z\to -0.$
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/0904.2078
dc.identifierhttp://arxiv.org/abs/0904.2078
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/228394
dc.subjectFunctional Analysis
dc.subjectSpectral Theory
dc.subject81Q10; 35P20; 47N50
dc.titleDiscrete Spectrum of a Model Operator Related to Three-Particle Discrete Schrödinger Operators
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