On the essential and discrete spectrum of a model operator related to three-particle discrete Schrödinger operators

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dc.creatorAlbeverio, Sergio
dc.creatorLakaev, Saidakhmat N.
dc.creatorDjumanova, Ramiza Kh.
dc.date2005-01-11
dc.date.accessioned2026-07-07T04:31:48Z
dc.date.available2026-07-07T04:31:48Z
dc.descriptionA model operator $H$ corresponding to a three-particle discrete Schrödinger operator on a lattice $\Z^3$ is studied. The essential spectrum is described via the spectrum of two Friedrichs models with parameters $h_α(p),$ $α=1,2,$ $p \in \T^3=(-π,π]^3.$ The following results are proven: 1) The operator $H$ has a finite number of eigenvalues lying below the bottom of the essential spectrum in any of the following cases: (i) both operators $h_α(0), α=1,2,$ have a zero eigenvalue; (ii) either $h_1(0)$ or $h_2(0)$ has a zero eigenvalue. 2) The operator $H$ has infinitely many eigenvalues lying below the bottom and accumulating at the bottom of the essential spectrum, if both operators $h_α(0),α=1,2,$ have a zero energy resonance.
dc.identifierhttps://arxiv.org/abs/math-ph/0501024
dc.identifierhttp://arxiv.org/abs/math-ph/0501024
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57952
dc.subjectMathematical Physics
dc.subjectSpectral Theory
dc.subjectPrimary: 81Q10, Secondary: 35P20, 47N50
dc.titleOn the essential and discrete spectrum of a model operator related to three-particle discrete Schrödinger operators
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