Spectral theory of Toeplitz and Wiener-Hopf operators

Toeplitz 和 Wiener-Hopf 算子的谱理论

• 批准号: EP/M009475/1
• 负责人: Eugene Shargorodsky
• 金额: $ 4.13万
• 依托单位: King's College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2014
• 资助国家: 英国
• 起止时间: 2014 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FM009475%2F1
• 关键词: Spectral; theory; Toeplitz; Wiener; Hopf

There are at least two reasons for the continuous and increasing interest in the Riemann-Hilbert problem, Toeplitz and Wiener-Hopf operators. The first one is that the methods of the Riemann-Hilbert problem represent a universal and a most powerful tool that has been applied to a wide variety of problems in elasticity theory, fluid dynamics, physics, geometry, combinatorics, integrable systems, orthogonal polynomials, random matrices, probability and stochastic processes, information and control theory, and in many other fields. On the other hand, Toeplitz and Wiener-Hopf operators constitute one of the most important classes of non-self-adjoint operators with a very rich spectral theory, which utilizes methods of operator theory, function theory and the theory of Banach algebras.We intend to achieve a breakthrough in the study of a very wide class of Toeplitz operators. We also intend to make a major contribution to the study of asymptotic behaviour for truncated Wiener-Hopf operators, which is a field attracting a great deal of interest at present.

至少有两个原因引起人们对Riemann-Hilbert问题，Toeplitz和Wiener-Hopf运营商的持续兴趣。第一个是Riemann-Hilbert问题的方法代表了一种通用和最强大的工具，该工具已应用于弹性理论，流体动力学，物理学，几何学，组合系统，可集成系统，正交多种元素，随机矩阵，随机矩阵，预测性和信息性过程，信息性过程，信息和信息信息，信息和控制理论以及许多其他领域以及许多其他领域以及许多其他许多领域。另一方面，Toeplitz和Wiener-Hopf操作员构成了具有非常丰富的光谱理论的最重要的非自身辅助操作符的类别之一，该类别利用了Banach代数的操作符理论，功能理论和理论的方法。我们还打算为截断的维纳·HOPF操作员对渐近行为的研究做出重大贡献，这是一个目前引起了极大兴趣的领域。

项目成果

Maximum norm versions of the Szego and Avram-Parter theorems for Toeplitz matrices

Toeplitz 矩阵的 Szego 和 Avram-Parter 定理的最大范数版本

• DOI: 10.1016/j.jat.2015.03.003
• 发表时间: 2015
• 期刊: Journal of Approximation Theory
• 影响因子: 0.9
• 作者: Bogoya J

Asymptotics of eigenvalues of symmetric Toeplitz band matrices

对称Toeplitz带矩阵特征值的渐近

• DOI: 10.1016/j.laa.2014.11.034
• 发表时间: 2015
• 期刊: Linear Algebra and its Applications
• 影响因子: 1.1
• 作者: Batalshchikov A

Eigenvectors of Hermitian Toeplitz matrices with smooth simple-loop symbols

• DOI: 10.1016/j.laa.2015.12.017
• 发表时间: 2016-03-15
• 期刊: LINEAR ALGEBRA AND ITS APPLICATIONS
• 影响因子: 1.1
• 作者: Bogoya, J. M.;Boettcher, A.;Maximenko, E. A.
• 通讯作者: Maximenko, E. A.

Asymptotics of Eigenvectors of Large Symmetric Banded Toeplitz Matrices

大对称带状Toeplitz矩阵特征向量的渐近性

• DOI: 10.1007/s00020-015-2257-y
• 发表时间: 2015
• 期刊: Integral Equations and Operator Theory
• 影响因子: 0.8
• 作者: Batalshchikov A