On the number of eigenvalues of a model operator associated to a system of three-particles on lattices |
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Authors: | S Albeverio S N Lakaev Z I Muminov |
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Institution: | 1.Institut für Angewandte Mathematik,Universit?t Bonn,Bonn,Germany;2.Samarkand State University,Samarkand,Uzbekistan;3.Samarkand Division of Academy of Sciences of Uzbekistan,Uzbekistan |
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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
hma 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
hma h_{\mu _\alpha }
(0), α = 1, 2, has a threshold eigenvalue. |
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Keywords: | |
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