Generalized spectra of differential operators can be related to spectra of preconditioned discretized operators. Obtaining (estimates of) the eigenvalues of the preconditioned discretized operators may lead to better estimating of the quality of preconditioners. In this short paper, we answer the open question posted in the recent paper Generalized spectrum of second order differential operators, authored by Gergelits, Nielsen, and Strako\v s. The proof we present allows us to fully extend characterizing the generalized spectra of $\nabla\cdot K\nabla u=\lambda\triangle u$ to problems of dimension three or higher.

翻译：微分算子的广义谱可与预处理离散化算子的谱相关联。获取预处理离散化算子的特征值（估计值）有助于更精确地评估预处理器的质量。本文对Gergelits、Nielsen和Strakoš在近期论文《二阶微分算子的广义谱》中提出的开放性问题给出解答。我们提出的证明方法将$\nabla\cdot K\nabla u=\lambda\triangle u$的广义谱表征完全推广至三维及更高维度问题。