论文标题
szegő型定理和符号特征值的分布
A Szegő type theorem and distribution of symplectic eigenvalues
论文作者
论文摘要
我们根据其生成功能研究固定G链的特性。特别是，我们证明了Szegő限制了符号特征值定理的类似物，得出了固定量子高斯过程的熵速率的表达，并研究了截短的块状toeplitz矩阵的符号特征值的分布。我们还引入了一个类似于数值范围的象征数值范围的概念，并研究了其一些基本属性，主要是在块Toeplitz运算符的背景下。
We study the properties of stationary G-chains in terms of their generating functions. In particular, we prove an analogue of the Szegő limit theorem for symplectic eigenvalues, derive an expression for the entropy rate of stationary quantum Gaussian processes, and study the distribution of symplectic eigenvalues of truncated block Toeplitz matrices. We also introduce a concept of symplectic numerical range, analogous to that of numerical range, and study some of its basic properties, mainly in the context of block Toeplitz operators.
