FROM CRYSTAL OPTICS TO DIRAC OPERATORS: A SPECTRAL THEORY OF FIRST-ORDER SYSTEMS
First-order systems of partial differential equations appear
in many areas of physics, from the Maxwell equations to the Dirac
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).