Spectral projection, residue of the scattering amplitude and Schrödinger group expansion for barrier-top resonances
Language
en
Article de revue
This item was published in
Annales de l'Institut Fourier. 2011, vol. 61, n° 4, p. 1351-1406
Association des Annales de l'Institut Fourier
English Abstract
We study the spectral projection associated to a barrier-top resonance for the semiclassical Schrodinger operator. First, we prove a resolvent estimate for complex energies close to such a resonance. Using that estimate ...Read more >
We study the spectral projection associated to a barrier-top resonance for the semiclassical Schrodinger 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 give an expansion for large times of the Schrodinger group in terms of these resonances.Read less <
Origin
Hal imported