Microlocalization of resonant states and estimates of the residue of the scattering amplitude (Q1889929)

The authors obtain microlocal estimates of the resonant states associated to a resonance, \(z_0\) of an \(h\)-differential operator. They show that the normalized resonant states are \(O(\sqrt{| \Im z_0| /h }+h^{\infty})\) outside the set of trapped trajectories and are \(O(h^{\infty})\) in the incoming area of phase space. Using these results they prove that the residue of the scattering amplitude of a Schrödinger operator is small in some directions under an estimate of the norm of the spectral projector.