Journal of Operator Theory

Volume 70, Issue 1, Summer 2013 pp. 109-144.

Weighted Mourre's commutator theory, application to Schroedinger operators with oscillating potential

Authors: Sylvain Golenia (1) and Thierry Jecko (2)
Author institution: (1) Universite de Bordeaux 1, Talence, F-33405, France
(2) AGM, UMR CNRS 8088, Universite de Cergy-Pontoise, Cergy-Pontoise, F-95000, France

Summary: We present a variant of Mourre's commutator theory. We apply it to prove the limiting absorption principle for Schroedinger operators with a perturbed Wigner--von Neumann potential at suitable energies. To our knowledge, this result is new since we allow a long range perturbation of the Wigner-von Neumann potential. Furthermore, we can show that the usual Mourre theory, based on differential inequalities and on the generator of dilation, cannot apply to our Schroedinger operators.

DOI: http://dx.doi.org/10.7900/jot.2011may06.1922
Keywords: Mourre's commutator theory, Mourre estimate, limiting absorption principle, continuous spectrum, Schroedinger operators, Wigner-von Neumann potential

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