THE LIMITING ABSORPTION PRINCIPLE FOR THE DISCRETE WIGNER-VON NEUMANN OPERATOR
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Resumen en inglés
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 ...Leer más >
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.< Leer menos
Palabras clave en inglés
Wigner-von Neumann potential
limiting absorption principle
discrete Schrödinger operator
Mourre theory
weighted Mourre theory
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