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Article Dans Une Revue Journal of Operator Theory Année : 2013

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

Sylvain Golenia
Thierry Jecko
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Résumé

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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Dates et versions

hal-00542694 , version 1 (03-12-2010)
hal-00542694 , version 2 (17-01-2011)
hal-00542694 , version 3 (01-06-2012)

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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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