Spectral Properties of Some Complex Jacobi Matrices
Spectral Properties of Some Complex Jacobi Matrices
复制标题
一些复雅可比矩阵的谱特性
DOI：
--
复制
发表时间：
2019
影响因子：
0.8
通讯作者：
Grzegorz Świderski
中科院分区：
文献类型：
--
作者：
Grzegorz Świderski
研究了有界复Jacobi矩阵和无界复Jacobi矩阵的谱性质。特别地，我们给出了所研究的算子的谱在复平面的某些子集上连续的条件，并给出了它们的广义特征向量的一致渐近性。我们通过考虑几类实Jacobi矩阵的复扰动来说明我们的结果：渐近周期、周期调制以及这两者的混合。此外，我们还给出了唯一闭扩张存在的条件。证明的方法是基于对移位的图兰行列式在复杂背景下的推广的分析。
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.