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We consider discrete Schr{\"o}dinger operators on ${\mathbb{Z}}^d$ for whichthe perturbation consists of the sum of a long-range type potential and aWigner-von Neumann type potential. Still working in a framework of weightedMourre theory, we improve the limiting absorption principle (LAP) that wasobtained in [Ma1]. To our knowledge, this is a new result even in theone-dimensional case. The improvement consists in a weakening of theassumptions on the long-range potential and better LAP weights. The improvementrelies only on the fact that the generator of dilations (which serves asconjugate operator) is bounded from above by the position operator. To exploitthis, Loewner's theorem on operator monotone functions is invoked.

Limiting absorption principle for discrete Schr{\"o}dinger operators with a Wigner-von Neumann potential and a slowly decaying potential