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arXiv · 1407.8299

Microlocal properties of scattering matrices

Shu Nakamura
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Abstract

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 $-μ$, $μ>1$. 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 Schrödigner operators, but it also applies to various differential operators with constant coefficients and short-range perturbations on Euclidean spaces.

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Shu Nakamura. 2014-07-31. Microlocal properties of scattering matrices. https://arxiv.org/abs/1407.8299

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