Mathematics

We provide a suitable extension of the theory of abstract Friedrichs systems from
real Hilbert spaces to the complex Hilbert space setting, which allows for applications
to partial differential equations with complex coeffcients. We also provide examples
where the involved Hilbert space is not the space of square integrable functions, as it
was the case in previous works, but rather its closed subspace or the space Hs(Rd;Cr),
for real s. This setting appears to be suitable for particular systems of partial differential
equations, such as the Dirac system, the Dirac-Klein-Gordon system, the Dirac-Maxwell
system, and the time-harmonic Maxwell system, which are all addressed in the paper.
Moreover, for the time-harmonic Maxwell system we also applied a suitable version of
the two-field theory with partial coercivity assumption which is developed in the paper.