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A Szegő type theorem and distribution of symplectic eigenvalues
Journal of Spectral Theory ( IF 1.0 ) Pub Date : 2021-09-28 , DOI: 10.4171/jst/377
Rajendra Bhatia 1 , Tanvi Jain 2 , Ritabrata Sengupta 3
Affiliation  

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.

中文翻译:

辛特征值的 Szegő 型定理和分布

我们根据生成函数研究固定 G 链的特性。特别是,我们证明了辛特征值的 Szegő 极限定理的类似物,推导了稳态量子高斯过程的熵率的表达式,并研究了截断块 Toeplitz 矩阵的辛特征值的分布。我们还引入了一个类似于数值范围的辛数值范围的概念,并主要在块 Toeplitz 算子的上下文中研究了它的一些基本性质。
更新日期:2021-10-07
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