Sharp exponential bounds on resonances states and width of resonances (Q1107075)

The paper is a contribution to a geometrical theory of resonances. It deals with potentials of certain geometrical shapes in the quasiclassical regime. The main result is the proof of existence of resonances and estimates of the width of resonances in terms of geodesic distances determined by the potential (instanton actions). The Agmon-type approach is used and a perturbative argument provides exponential bounds on the resonances states. These results are applied to the shape and Stark resonances and give a partial generalization of the classical Oppenheimer formula derived original for the hydrogen atom.