BONY, Jean Francois; FUJIIE, Setsuro; RAMOND, Thierry; ZERZERI, Maher

doi:10.5802/aif.2643

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BONY, Jean Francois
Institut de Mathématiques de Bordeaux [IMB]

FUJIIE, Setsuro
Graduate School of Material Science

RAMOND, Thierry
Laboratoire de Mathématiques d'Orsay [LMO]

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Annales de l'Institut Fourier. 2011, vol. 61, n° 4, p. 1351-1406

Association des Annales de l'Institut Fourier

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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.< Leer menos

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

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