11-117 S. Richard, R. Tiedra de Aldecoa

Spectral analysis and time-dependent scattering theory on manifolds with asymptotically cylindrical ends (488K, pdf) Aug 25, 11

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Abstract. We review the spectral analysis and the time-dependent approach of scattering theory for manifolds with asymptotically cylindrical ends. For the spectral analysis, higher order resolvent estimates are obtained via Mourre theory for both short-range and long-range behaviors of the metric and the perturbation at infinity. For the scattering theory, the existence and asymptotic completeness of the wave operators is proved in a two-Hilbert spaces setting. A stationary formula as well as mapping properties for the scattering operator are derived. The existence of time delay and its equality with the Eisenbud-Wigner time delay is finally presented. Our analysis mainly differs from the existing literature on the choice of a simpler comparison dynamics as well as on the complementary use of time-dependent and stationary scattering theories.

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