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 Weighted Mourres commutator theory, application to Schrödinger operators with oscillating potential


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We present a variant of Mourres 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.



Author: Sylvain Golenia; Thierry Jecko

Source: https://archive.org/



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