Microlocal properties of scattering matrices
58 mins 30 secs,
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About this item
| Description: |
Nakamura, S (University of Tokyo)
Thursday 09 April 2015, 10:00-11:00 |
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| Created: | 2015-04-13 10:58 |
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| Collection: | Periodic and Ergodic Spectral Problems |
| Publisher: | Isaac Newton Institute |
| Copyright: | Nakamura, S |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | We consider scattering theory for a pair of operators H0 and H=H0+V on L2(M,m), where M is a Riemannian manifold, H0 is a multiplication operator on M and V is a pseudodifferential operator of order −μ, μ>1. We show that a time-dependent scattering theory can be constructed, and the scattering matrix is a pseudodifferential operator on each energy surface. Moreover, the principal symbol of the scattering matrix is given by a Born approximation type function. The main motivation of the study comes from applications to discrete Schr\"odigner operators, but it also applies to various differential operators with constant coefficients and short-range perturbations on Euclidean spaces. |
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