非对称扰动雅可比矩阵序列谱的渐近性质
The asymptotic properties of the spectrum of non symmetrically perturbed Jacobi matrix sequences
AI总结：
在温和迹范数假设下，证明非厄米复扰动下雅可比矩阵序列的特征值仍由实值函数 $2\cos t$ 在 $[0,\pi]$ 上分布，且 $[-2,2]$ 强吸引扰动矩阵序列。
摘要：
在温和的迹范数假设下，我们证明了一个一般的（非厄米的）复扰动雅可比矩阵序列（不一定是实的）的特征值仍然由实值函数 $2\cos t$ 在 $[0,\pi]$ 上分布，这刻画了未扰动的情况。这样，实区间 $[-2,2]$ 仍然是渐近联合谱的聚点，而且 $[-2,2]$ 强吸引（无限阶）扰动矩阵序列。这些结果直接由我们在渐近线性代数框架中证明的更一般事实得出，并且可以简单地推广到矩阵值符号的情形，这出现在处理具有渐近周期递归系数的正交多项式时。
英文摘要：
Under the mild trace-norm assumptions we show that the eigenvalues of a generic (non Hermitian) complex perturbation of a Jacobi matrix sequence (not necessarily real) are still distributed as the real-valued function $2\cos t$ on $[0,π]$, which characterizes the nonperturbed case. In this way the real interval $[-2,2]$ is still a cluster for the asymptotic joint spectrum and, moreover, $[-2,2]$ attracts strongly (with infinite order) the perturbed matrix sequence. The results follow in a straightforward way from more general facts that we prove in an asymptotic linear algebra framework and are plainly generalized to the case of matrix-valued symbol, which arises when dealing with orthogonal polynomials with asymptotically periodic recurrence coefficients.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
