TY - RPRT
T1 - Complex Friedrichs systems and applications
Y1 - 2017
A1 - Nenad Antonić
A1 - Krešimir Burazin
A1 - Ivana Crnjac
A1 - Marko Erceg
AB - 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.
UR - http://urania.sissa.it/xmlui/handle/1963/35270
U1 - 35576
U2 - Mathematics
U4 - 1
ER -
TY - RPRT
T1 - On contact interactions realised as Friedrichs systems
Y1 - 2017
A1 - Marko Erceg
A1 - Alessandro Michelangeli
AB - 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.
UR - http://preprints.sissa.it/handle/1963/35298
U1 - 35604
U2 - Mathematics
U4 - 1
ER -
TY - RPRT
T1 - Friedrichs systems in a Hilbert space framework: solvability and multiplicity
Y1 - 2017
A1 - Nenad Antonić
A1 - Marko Erceg
A1 - Alessandro Michelangeli
AB - 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 Antonić 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.
UR - http://preprints.sissa.it/handle/1963/35280
U1 - 35587
U2 - Mathematics
U4 - 1
ER -