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.

人们对黎曼-希尔伯特问题持续且日益增长的兴趣至少有两个原因：托普利茨算子和维纳-霍普夫算子。第一个是黎曼-希尔伯特问题的方法代表了一种通用且最强大的工具，已应用于弹性理论、流体动力学、物理学、几何、组合学、可积系统、正交多项式等领域的各种问题，随机矩阵、概率和随机过程、信息和控制理论以及许多其他领域。另一方面，Toeplitz 和 Wiener-Hopf 算子构成了最重要的一类非自伴算子，具有非常丰富的谱理论，它利用了算子理论、函数论和 Banach 代数理论的方法。在广泛的托普利茨算子的研究中取得突破。我们还打算为截断 Wiener-Hopf 算子渐近行为的研究做出重大贡献，这是目前引起人们极大兴趣的领域。

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

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

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.