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

Let Omega subset of 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.