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

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

2010-12-03

arxiv.org/abs/1012.0705v2

Mathematics

Spectral Theory

New title. Text greatly improved. Many details added. Remark 5.6 is new

Scientific paper

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

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