@article {2017,
	title = {Complex Friedrichs systems and applications},
	number = {SISSA;03/2017/MATE},
	year = {2017},
	abstract = {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.},
	url = {http://urania.sissa.it/xmlui/handle/1963/35270},
	author = {Nenad Antoni{\'c} and Kre{\v s}imir Burazin and Ivana Crnjac and Marko Erceg}
}
@article {2017,
	title = {On contact interactions realised as Friedrichs systems},
	number = {SISSA;48/2017/MATE},
	year = {2017},
	abstract = {We 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.},
	url = {http://preprints.sissa.it/handle/1963/35298},
	author = {Marko Erceg and Alessandro Michelangeli}
}
@article {2017,
	title = {Friedrichs systems in a Hilbert space framework: solvability and multiplicity},
	number = {SISSA;16/2017/MATE},
	year = {2017},
	abstract = {The Friedrichs (1958) theory of positive symmetric systems of first order partial
differential equations encompasses many standard equations of mathematical physics, irrespective of their type. This theory was recast in an abstract Hilbert space setting by Ern, Guermond and Caplain (2007), and by Antoni{\'c} and Burazin (2010). In this work we make a further step, presenting a purely operator-theoretic description of abstract Friedrichs systems, and proving that any pair of abstract Friedrichs operators admits bijective extensions with a signed boundary map. Moreover, we provide suffcient and necessary conditions for existence of infinitely many such pairs of spaces, and by the universal operator extension theory (Grubb, 1968) we get a complete identification of all such pairs, which we illustrate on two concrete one-dimensional examples.},
	url = {http://preprints.sissa.it/handle/1963/35280},
	author = {Nenad Antoni{\'c} and Marko Erceg and Alessandro Michelangeli}
}
