某些周期三对角算子的数值域是两个有限矩阵的数值域的凸包
The numerical range of some periodic tridiagonal operators is the convex hull of the numerical ranges of two finite matrices
摘要：
本文证明了前两位作者提出的一个猜想，即建立了一类$n+1$ -周期三对角算子的数值域的闭包为两个三对角$(n+1) \times (n+1)$矩阵的数值域的凸包。此外，当$n+1$是奇数时，我们证明了这样的矩阵的大小简化为$\frac{n}{2}+1$。
英文摘要：
In this paper we prove a conjecture stated by the first two authors establishing the closure of the numerical range of a certain class of $n+1$-periodic tridiagonal operators as the convex hull of the numerical ranges of two tridiagonal $(n+1) \times (n+1)$ matrices. Furthermore, when $n+1$ is odd, we show that the size of such matrices simplifies to $\frac{n}{2}+1$.
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。
