Jordan chains of elliptic partial differential operators and Dirichlet-to-Neumann maps (Q2078206)

Summary: Let \(\Omega \subset \mathbb{R}^d\) be a bounded open set with Lipschitz boundary \(\Gamma \). It will be shown that the Jordan chains of m-sectorial second-order elliptic partial differential operators with measurable coefficients and (local or non-local) Robin boundary conditions in \(L_2(\Omega)\) can be characterized with the help of Jordan chains of the Dirichlet-to-Neumann map and the boundary operator from \(H^{1/2}(\Gamma)\) into \(H^{-1/2}(\Gamma)\). This result extends the Birman-Schwinger principle in the framework of elliptic operators for the characterization of eigenvalues, eigenfunctions and geometric eigenspaces to the complete set of all generalized eigenfunctions and algebraic eigenspaces.