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

Sylvain Golenia (1) , Thierry Jecko (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

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.

Domains: Spectral Theory [math.SP]; Analysis of PDEs [math.AP]; Functional Analysis [math.FA]

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⟩