对数支割在非自伴算子谱行列式定义中的作用
The role of the branch cut of the logarithm in the definition of the spectral determinant for non-selfadjoint operators
AI总结：
本文研究非自伴算子谱行列式对复对数支割选择的依赖，给出行列式可否定义及其取值随支割变化的判定结果。
摘要：
谱行列式通常借助亚纯延拓至零点的谱 zeta 函数来定义。在此定义中，会出现特征值的复对数。因此，谱行列式的概念取决于人们在定义对数时如何选择支割。我们给出了关于非自伴算子的结果，说明行列式何时可以定义、何时不能定义，以及其值如何随支割选择而不同。
英文摘要：
The spectral determinant is usually defined using the spectral zeta function that is meromorphically continued to zero. In this definition, the complex logarithms of the eigenvalues appear. Hence the notion of the spectral determinant depends on the way how one chooses the branch cut in the definition of the logarithm. We give results for the non-self-adjoint operators that state when the determinant can and cannot be defined and how its value differs depending on the choice of the branch cut.
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