论文标题
具有复杂参数的KAC-Murdock-Szego矩阵中的特征值分叉
Eigenvalue bifurcations in Kac-Murdock-Szego matrices with a complex parameter
论文作者
论文摘要
对于复杂的$ρ$，toeplitz矩阵的光谱属性$ k_ {n}（ρ）= \ left [ρ^{| j-k |} \ right] _ {j，j，k = 1}^{n} $，通常称为kac-murdock-szeg-szeg-szeg matrix，已在最近的纸张中进行了研究。尤其是第二篇论文引入了边界曲线的概念。这是复合$ρ$平面中的两个封闭曲线，由$ k_n（ρ）$的所有$ρ$组成，其幅度等于矩阵尺寸$ n $。本文的目的是以定性和定量方式检查特征值分叉，并讨论分叉与边界曲线之间的联系。
For complex $ρ$, the spectral properties of the Toeplitz matrix $K_{n}(ρ)=\left[ρ^{|j-k|}\right]_{j,k=1}^{n}$, often called the Kac-Murdock-Szegο matrix, have been examined in detail in two recent papers. The second paper, in particular, introduced the concept of borderline curves. These are two closed curves in the complex-$ρ$ plane that consist of all the $ρ$ for which $K_n(ρ)$ possesses some eigenvalue whose magnitude equals the matrix dimension $n$. The purpose of the present paper is to examine eigenvalue bifurcations in both a qualitative and a quantitative manner, and to discuss connections between bifurcations and the borderline curves.
