01282nas a2200133   4500008004100000245004800041210004800089520088200137100002001019700002301039700001801062700001701080856005101097       2017                        en  d00aComplex Friedrichs systems and applications0 aComplex Friedrichs systems and applications3 aWe 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.1 aAntonić, Nenad1 aBurazin, Krešimir1 aCrnjac, Ivana1 aErceg, Marko  uhttp://urania.sissa.it/xmlui/handle/1963/3527000871nas a2200109   4500008004100000245005900041210005600100520051100156100001700667700002900684856004800713       2017                        en  d00aOn contact interactions realised as Friedrichs systems0 acontact interactions realised as Friedrichs systems3 aWe realise the Hamiltonians of contact interactions in quantum mechanics within the framework of abstract Friedrichs systems. In particular, we show that the construction of the self-adjoint (or even only closed) operators of contact interaction supported at a fixed point can be associated with the construction of the bijective realisations of a suitable pair of abstract Friedrich operators. In this respect, the Hamiltonians
of contact interaction provide novel examples of abstract Friedrich systems.1 aErceg, Marko1 aMichelangeli, Alessandro  uhttp://preprints.sissa.it/handle/1963/35298