On the number of eigenvalues of a model operator associated to a system of three-particles on lattices
Albeverio, Sergio ; Lakaev, Saidakhmat N. ; Muminov, Zahriddin I.
arXiv, 0508029 / Harvested from arXiv
Text on arXiv
A model operator $H$ associated to a system of three-particles on the three dimensional lattice $\Z^3$ and interacting via pair non-local potentials is studied. The following results are proven: (i) the operator $H$ has infinitely many eigenvalues lying below the bottom of the essential spectrum and accumulating at this point, in the case, where both Friedrichs model operators $h_{\mu_\alpha}(0),\alpha=1,2,$ have threshold resonances. (ii) the operator $H$ has a finite number of eigenvalues lying outside of the essential spectrum, in the case, where at least one of $h_{\mu_\alpha}(0), \alpha=1,2,$ has a threshold eigenvalue.
Publié le : 2005-08-14
Classification:  Mathematical Physics,  Mathematics - Spectral Theory,  Primary: 81Q10, Secondary: 35P20, 47N50 
@article{0508029,
     author = {Albeverio, Sergio and Lakaev, Saidakhmat N. and Muminov, Zahriddin I.},
     title = {On the number of eigenvalues of a model operator associated to a system
  of three-particles on lattices},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0508029}
}

Albeverio, Sergio; Lakaev, Saidakhmat N.; Muminov, Zahriddin I. On the number of eigenvalues of a model operator associated to a system
  of three-particles on lattices. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0508029/