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.

中文翻译：

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椭圆偏微分算子的 Jordan 链和 Dirichlet-to-Neumann 映射

令 $\Omega \subset \mathbb{R}^d$ 是一个具有 Lipschitz 边界 $\Gamma$ 的有界开集。将证明 $L_2(\Omega)$ 中具有可测系数和（局部或非局部）Robin 边界条件的 m 扇区二阶椭圆偏微分算子的 Jordan 链可以在 Jordan 链的帮助下表征Dirichlet-to-Neumann 映射和边界算子从 $H^{1/2}(\Gamma)$ 到 $H^{-1/2}(\Gamma)$。该结果将用于表征特征值、特征函数和几何特征空间的椭圆算子框架中的 Birman-Schwinger 原理扩展到所有广义特征函数和代数特征空间的完整集合。