2017/06/06 by Fischbacher, Christoph · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1706.01904
We consider dissipative operators A of the form A=S+iV, where both S and V≥ 0 are assumed to be symmetric but neither of them needs to be (essentially) selfadjoint. After a brief discussion of the relation of the operators S± iV to dual pairs with the so called common core property, we present a necessary and suffcient condition for any extension of A with domain contained in D((S-iV)^*) to be dissipative. We will discuss several special situations in which this condition can be expressed in a particularly nice form -- accessible to direct computations. Examples involving ordinary differential operators are given.