01281nas a2200121 4500008004100000245008200041210006900123520085300192100002001045700001701065700002901082856004801111 2017 en d00aFriedrichs systems in a Hilbert space framework: solvability and multiplicity0 aFriedrichs systems in a Hilbert space framework solvability and 3 aThe 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 AntoniÄ‡ 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.1 aAntoniÄ‡, Nenad1 aErceg, Marko1 aMichelangeli, Alessandro uhttp://preprints.sissa.it/handle/1963/35280