The classical concept of Q-functions associated to symmetric and selfadjoint operators due to M.G. Krein and H. Langer 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. For couplings of uniformly elliptic second order differential expression on bounded and unbounded domains explicit Krein type formulas for the difference of the resolvents and trace formulas in an H2-framework are obtained.
D. Alpay and J. Behrndt. Generalized Q-functions and Dirichlet-to-Neumann maps for elliptic differential operators. Journal of Functional Analysis, vol. 257 (2009), no. 6, pp. 1666-1694.
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.