hal-00542694, version 1
Rescaled 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.
- 1:
- Université Sciences et Technologies - Bordeaux I
- 2:
- CNRS : UMR8088 – Université de Cergy Pontoise
- Domain : Mathematics/Spectral Theory
Mathematics/Analysis of PDEsMathematics/Functional Analysis - Available versions : v1 (2010-12-03) v2 (2011-01-18) v3 (2012-06-01)
- hal-00542694, version 1
- http://hal.archives-ouvertes.fr/hal-00542694
- oai:hal.archives-ouvertes.fr:hal-00542694
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- Submitted on: Friday, 3 December 2010 11:47:11
- Updated on: Friday, 3 December 2010 12:25:31
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