V. Bach, W. de Siqueira Pedra, and S. N. Lakaev
Bounds on the Pure Point Spectrum of Lattice 
Schr dinger Operators
(269K, pdf)

ABSTRACT.  In dimension d≥3 a variational principle for the size of the pure point 
spectrum, thus taking embedded eigenvalues into account, of Schr dinger 
operators H(e,V) on the lattice is proven. The dispersion relations e are assumed to be Morse functions and the potentials V(x) to decay faster than 
|x|^{−2(d+3)}, but are not necessarily of definite sign. The proof is based on resolvent estimates for H(e,V′), for small V′, combined with positivity arguments.