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.

有至少两个原因，连续和越来越多的兴趣在黎曼-希尔伯特问题，Toeplitz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个普遍的和最强大的工具，它已被应用于弹性理论，流体动力学，物理学，几何学，组合学，可积系统，正交多项式，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的各种问题。另一方面，Toeplitz算子和Wiener-Hopf算子构成了一类重要的非自伴算子，它们的谱理论非常丰富，本文利用算子论、函数论和Banach代数理论的方法，试图在广泛的一类Toeplitz算子的研究中取得突破性的进展。我们还打算作出重大贡献的截断Wiener-Hopf算子，这是一个领域吸引了大量的兴趣，目前的渐近行为的研究。

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.