THE LIMITING ABSORPTION PRINCIPLE FOR THE DISCRETE WIGNER-VON NEUMANN OPERATOR

Marc-Adrien Mandich (1)

1 IMB - Institut de Mathématiques de Bordeaux

We apply weighted Mourre commutator theory to prove the limiting absorption principle for the discrete Schrödinger 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 Schrödinger operators.

Mots clés: Wigner-von Neumann potential; limiting absorption principle; discrete Schrödinger operator; Mourre theory; weighted Mourre theory

Domaines: Théorie spectrale [math.SP]; Physique mathématique [math-ph]; Analyse fonctionnelle [math.FA]

Marc-Adrien Mandich. THE LIMITING ABSORPTION PRINCIPLE FOR THE DISCRETE WIGNER-VON NEUMANN OPERATOR. 2016. ⟨hal-01297239⟩