Seminario di fisica matematica
ore
16:00
presso Seminario I
We study the spectral projection associated to a
barrier-top resonance for the semi-classical Schroedinger operator. First, we prove a resolvent estimate for complex energies close to such a resonance. Using this estimate and an explicit representation of the resonant states, we
show that the spectral projection has a semi-classical expansion in integer powers of h and compute its leading term. We use this result to compute the residue of the scattering amplitude at a resonance. We also give an expansion of the Schroedinger group in terms of these resonances.