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SUMMARY:Microlocal properties of scattering matrices - Nakamura\, S (Unive
 rsity of Tokyo)
DTSTART:20150409T090000Z
DTEND:20150409T100000Z
UID:TALK58820@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We consider scattering theory for a pair of operators $H_0$ an
 d $H=H_0+V$ 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 ope
 rator on each energy surface. Moreover\, the principal symbol of the scatt
 ering matrix is given by a Born approximation type function. The main moti
 vation of the study comes from applications to discrete Schr"odigner opera
 tors\, but it also applies to various differential operators with constant
  coefficients and short-range perturbations on Euclidean spaces.\n
LOCATION:Seminar Room 1\, Newton Institute
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