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

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