On the essential and discrete spectrum of a model operator related to three-particle discrete Schrödinger operators
Sergio Albeverio, Saidakhmat N. Lakaev, Ramiza Kh. Djumanova
Abstract
A model operator H corresponding to a three-particle discrete Schrödinger operator on a lattice 3 is studied. The essential spectrum is described via the spectrum of two Friedrichs models with parameters hα(p), α=1,2, p ∈ 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 hα(0), α=1,2, have a zero eigenvalue; (ii) either h1(0) or h2(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 hα(0),α=1,2, have a zero energy resonance.
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