塞格格型定理与辛特征值的分布

IF 1 3区数学 Q1 MATHEMATICS

Journal of Spectral Theory Pub Date : 2020-06-21 DOI:10.4171/JST/377

R. Bhatia, Tanvi Jain, R. Sengupta

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引用次数: 3

摘要

我们从生成函数的角度研究了平稳G-链的性质。特别地，我们证明了辛特征值的Szegõ极限定理的类似性，导出了平稳量子高斯过程熵率的表达式，并研究了截断块Toeplitz矩阵的辛特征值分布。我们还引入了辛数值范围的一个概念，类似于数值范围的概念，并研究了它的一些基本性质，主要是在块Toeplitz算子的背景下。

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A Szegő type theorem and distribution of symplectic eigenvalues

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.

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来源期刊

Journal of Spectral Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

0.00%

发文量

期刊介绍： The Journal of Spectral Theory is devoted to the publication of research articles that focus on spectral theory and its many areas of application. Articles of all lengths including surveys of parts of the subject are very welcome. The following list includes several aspects of spectral theory and also fields which feature substantial applications of (or to) spectral theory. Schrödinger operators, scattering theory and resonances; eigenvalues: perturbation theory, asymptotics and inequalities; quantum graphs, graph Laplacians; pseudo-differential operators and semi-classical analysis; random matrix theory; the Anderson model and other random media; non-self-adjoint matrices and operators, including Toeplitz operators; spectral geometry, including manifolds and automorphic forms; linear and nonlinear differential operators, especially those arising in geometry and physics; orthogonal polynomials; inverse problems.