Abstract
A model operator H associated to a system of three particles on the threedimensional lattice ℤ3 that interact via nonlocal pair potentials is studied. The following results are established. (i) The operator H has infinitely many eigenvalues lying below the bottom of the essential spectrum and accumulating at this point if both the Friedrichs model operators \(h_{\mu _\alpha } \) (0), α = 1, 2, have threshold resonances. (ii) The operator H has finitely many eigenvalues lying outside the essential spectrum if at least one of the operators \(h_{\mu _\alpha } \) (0), α = 1, 2, has a threshold eigenvalue.
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Dedicated to the memory of Vladimir Geyler
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Albeverio, S., Lakaev, S.N. & Muminov, Z.I. On the number of eigenvalues of a model operator associated to a system of three-particles on lattices. Russ. J. Math. Phys. 14, 377–387 (2007). https://doi.org/10.1134/S1061920807040024
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DOI: https://doi.org/10.1134/S1061920807040024