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Spectral projection, residue of the scattering amplitude and Schrödinger group expansion for barrier-top resonances

Jean-François Bony;  Setsuro Fujiié;  Thierry Ramond;  Maher Zerzeri — 2011

Annales de l’institut Fourier

We study the spectral projection associated to a barrier-top resonance for the semiclassical Schrödinger operator. First, we prove a resolvent estimate for complex energies close to such a resonance. Using that estimate and an explicit representation of the resonant states, we show that the spectral projection has a semiclassical expansion in integer powers of h , and compute its leading term. We use this result to compute the residue of the scattering amplitude at such a resonance. Eventually, we...

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