The Mourre estimate in the semiclassical limit (Q920300)

This is a continuation of a series of papers by the author and others, discussing the relationship between a classical nontrapping condition and the absence of resonance. The author shows that the relationship between the positivity of a Poisson bracket localized on an energy shell and the Mourre estimate is based on the classical limit. But that between the Mourre estimate and the absence of resonance is not. In the process of establishing these results, it is also shown that the eigenstates decay exponentially in the classically forbidden region, (with suitable restriction on the potential).