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

Let Ω Rd be a bounded open set with Lipschitz boundary Γ. 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 L2.Ω/ can be characterized with the help of Jordan chains of the Dirichlet-to-Neumann map and the boundary operator from H1=2.Γ/ into H-1=2. Γ/. 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.