Resonances in domains of size \(h\) (Q2761855)

The author considers a self-adjoint unbounded operator \(P\) which tends to \((-h^2\Delta)\) at infinity and gives an estimation for the number of the resonances of \(P\) in domains of size \(h\) around a regular value \(E_0\). Here \(h\) stands for any number in the open interval \((0,1)\). The main result, which is stated as a theorem, shows that the number in question is of \(O(h^{1-n})\). In the proof, the definition of the resonances through the analytical dilatations method plays an important role.