Weighted Mourre's commutator theory, application to Schr\"odinger operators with oscillating potential

Sylvain Golenia; Thierry Jecko

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arXiv · 1012.0705

Weighted Mourre's commutator theory, application to Schr\"odinger operators with oscillating potential

Sylvain Golenia·Thierry Jecko

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Abstract

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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BibTeX RIS

Sylvain Golenia, Thierry Jecko. 2010-12-03. Weighted Mourre's commutator theory, application to Schr\"odinger operators with oscillating potential. https://arxiv.org/abs/1012.0705

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