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Article Dans Une Revue Annales de l'Institut Fourier Année : 2011

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

Résumé

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.

Dates et versions

hal-00994373 , version 1 (21-05-2014)

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Jean Francois Bony, Setsuro Fujiie, Thierry Ramond, Maher Zerzeri. Spectral projection, residue of the scattering amplitude and Schrödinger group expansion for barrier-top resonances. Annales de l'Institut Fourier, 2011, 61 (4), pp.1351-1406. ⟨10.5802/aif.2643⟩. ⟨hal-00994373⟩
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