On the essential and discrete spectrum of a model operator related to three-particle discrete Schr\"odinger operators
Albeverio, Sergio ; Lakaev, Saidakhmat N. ; Djumanova, Ramiza Kh.
arXiv, 0501024 / Harvested from arXiv
Text on arXiv
A model operator $H$ corresponding to a three-particle discrete Schr\"odinger operator on a lattice $\Z^3$ is studied. The essential spectrum is described via the spectrum of two Friedrichs models with parameters $h_\alpha(p),$ $\alpha=1,2,$ $p \in \T^3=(-\pi,\pi]^3.$ 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 $h_\alpha(0), \alpha=1,2,$ 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 $h_\alpha(0),\alpha=1,2,$ have a zero energy resonance.
Publié le : 2005-01-11
Classification:  Mathematical Physics,  Mathematics - Spectral Theory,  Primary: 81Q10, Secondary: 35P20, 47N50 
@article{0501024,
     author = {Albeverio, Sergio and Lakaev, Saidakhmat N. and Djumanova, Ramiza Kh.},
     title = {On the essential and discrete spectrum of a model operator related to
  three-particle discrete Schr\"odinger operators},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0501024}
}

Albeverio, Sergio; Lakaev, Saidakhmat N.; Djumanova, Ramiza Kh. On the essential and discrete spectrum of a model operator related to
  three-particle discrete Schr\"odinger operators. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0501024/