Studying spectral properties of operator polynomials is reduced to studying the corresponding spectral properties of operators defined by operator matrices. The results are used to investigate second-order differential operators by associating them with the corresponding first-order differential operators and using their properties related to invertibility.

中文翻译：

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算子多项式和二阶微分算子的谱分析

研究算子多项式的谱特性被简化为研究由算子矩阵定义的算子的相应谱特性。通过将它们与相应的一阶微分算子相关联并使用它们与可逆性有关的性质，将结果用于研究二阶微分算子。