Generalized \(Q\)-functions and Dirichlet-to-Neumann maps for elliptic differential operators (Q841494)

The notion of a \(Q\)-function associated with a pair \(\{S, A\}\) consisting of a symmetric operator \(S\) and a selfadjoint extension \(A\) of \(S\) in a Hilbert or Pontryagin space is extended in such a way that the Dirichlet-to-Neumann map in the theory of elliptic differential equations can be interpreted as a generalized \(Q\)-function. Krein type formulas for the difference of the resolvents of uniformly elliptic second-order differential expressions on bounded and unbounded domains are established, together with trace formulas in an \(H^2\) framework.