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The limiting absorption principle for the discrete Wigner-von Neumann operator (1605.00879v1)
Published 3 May 2016 in math.SP, math-ph, math.FA, and math.MP
Abstract: We apply weighted Mourre commutator theory to prove the limiting absorption principle for the discrete Schr{\"o}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{\"o}dinger operators.