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Microlocal properties of scattering matrices

Presented by: 
S Nakamura University of Tokyo
Thursday 9th April 2015 - 10:00 to 11:00
INI Seminar Room 1
We consider scattering theory for a pair of operators $H_0$ and $H=H_0+V$ on $L^2(M,m)$, where $M$ is a Riemannian manifold, $H_0$ is a multiplication operator on $M$ and $V$ is a pseudodifferential operator of order $-\mu$, $\mu>1$. 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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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons