From Crystal Optics to Dirac Operators: a Spectral Theory of First-Order Systems

Date(s) : 10/02/2015   iCal
11 h 00 min - 12 h 00 min

First-order systems of partial differential equations
appear in many areas of physics, from the Maxwell equations to the Dirac
operator.
The aim of the talk is to describe a general method for the study of
the spectral density of all such systems, connecting it to traces on the
(geometric-optical) « slowness surfaces » .
The Holder continuity of the spectral density leads to a derivation
of the limiting absorption principle and global spacetime estimates.
(based on joint work with Tomio Umeda).

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