The limiting absorption principle for the discrete Wigner-von Neumann operator
arXiv:1605.00879 · doi:10.1016/j.jfa.2016.09.022
Abstract
We apply weighted Mourre commutator theory to prove the limiting absorption principle for the discrete Schr{ö}dinger operator perturbed by the sum of a Wigner-von Neumann and long-range type potential. In particular, this implies a new result concerning the absolutely continuous spectrum for these operators even for the one-dimensional operator. We show that methods of classical Mourre theory based on differential inequalities and on the generator of dilation cannot apply to the mentionned Schr{ö}dinger operators.