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| HAL: hal-00660532, version 1 |
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| Spectral analysis and time-dependent scattering theory on manifolds with asymptotically cylindrical ends |
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| Serge Richard 1Rafael Tiedra De Aldecoa 2 |
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| (2012-01-17) |
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| 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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| 1: | Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
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| 2: | Facultad de Matematicas, Pontificia Universidad Catolica de Chile |
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Facultad de Matematicas, Pontificia Universidad Catolica de Chile |
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| PSPM |
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| Subject | : | Mathematics/Mathematical Physics |
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| Manifolds – spectral analysis – scattering theory – conjugate operator |
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| hal-00660532, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00660532 | |
| oai:hal.archives-ouvertes.fr:hal-00660532 | |
| From: Serge Richard | |
| Submitted on: Tuesday, 17 January 2012 01:55:08 | |
| Updated on: Tuesday, 17 January 2012 08:42:08 | |
