We study spectral properties of bounded and unbounded complex Jacobi matrices. In particular, we formulate conditions assuring that the spectrum of the studied operators is continuous on some subsets of the complex plane and we provide uniform asymptotics of their generalised eigenvectors. We illustrate our results by considering complex perturbations of real Jacobi matrices belonging to several classes: asymptotically periodic, periodically modulated and the blend of these two. Moreover, we provide conditions implying existence of a unique closed extension. The method of the proof is based on the analysis of a generalisation of shifted Turán determinants to the complex setting.

中文翻译：

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一些复数雅可比矩阵的光谱特性

我们研究有界和无界复雅可比矩阵的谱特性。特别是，我们制定了条件，确保所研究算子的频谱在复平面的某些子集上是连续的，并且我们提供了它们的广义特征向量的均匀渐近线。我们通过考虑属于几个类别的实际雅可比矩阵的复杂扰动来说明我们的结果：渐近周期性、周期性调制和这两者的混合。此外，我们提供了暗示存在唯一封闭扩展的条件。证明的方法是基于对转移 Turán 行列式对复杂设置的推广的分析。