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

Abstract : We present a variant of Mourre's commutator theory. We apply it to prove the limiting absorption principle for Schrödinger 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 Schrödinger operators.
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https://hal.archives-ouvertes.fr/hal-00542694
Contributor : Sylvain Golenia <>
Submitted on : Friday, June 1, 2012 - 2:51:00 PM
Last modification on : Thursday, May 6, 2021 - 10:16:44 AM
Long-term archiving on: : Sunday, September 2, 2012 - 2:38:16 AM

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Sylvain Golenia, Thierry Jecko. Weighted Mourre's commutator theory, application to Schrödinger operators with oscillating potential. Journal of Operator Theory, 2013, 1, J. Operator Theory 70 (2013), no. 1, 109-144. ⟨10.7900/jot.2011may06.1922⟩. ⟨hal-00542694v3⟩

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