Spectral Theory of Block Operator Matrices

分块算子矩阵的谱论

• 批准号: EP/E037844/1
• 负责人: Matthias Langer
• 金额: $ 24.43万
• 依托单位: University of Strathclyde
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2007
• 资助国家: 英国
• 起止时间: 2007 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FE037844%2F1
• 关键词: Spectral; Theory; Block; Operator; Matrices

Block operator matrices are matrices whose entries are operators in Hilbert or Banach spaces. Such operators appear in a natural way when systems of differential equations with different order and type are investigated or an operator in a given space is considered that has a natural decomposition intosubspaces. In many applications of mathematical physics it is natural and fruitful to use the theory of block operator matrices.It is the aim to study spectral properties of such block operator matrices: location of the essential spectrum, variational principles and estimates for eigenvalues, investigation of spectral subspaces, basis properties of components of eigenvectors and generalised Fourier transforms. Particular emphasis is placed on unbounded block operator matrices, for which different cases have to be considered separately; these cases depend on the places where the strongest operators are located.The results should be applied to concrete operators arising in applications, mainly ordinary or partial differential operators.

块算子矩阵是以Hilbert或Banach空间中的算子为输入的矩阵。当研究不同阶和不同类型的微分方程组时，或者考虑给定空间中具有自然分解到子空间的算子时，这种算子以一种自然的方式出现。在数学物理的许多应用中，利用分块算子矩阵的理论是自然而富有成效的，其目的是研究这类分块算子矩阵的谱性质：本质谱的位置、特征值的变分原理和估计、谱子空间的研究、特征向量分量的基本性质和广义傅立叶变换。特别强调了无界分块算子矩阵，对于这种矩阵，不同的情况必须分开考虑；这些情况取决于最强算子所在的位置。结果应该应用于应用中出现的具体算子，主要是普通或偏微分算子。

项目成果

Spectral estimates for resolvent differences of self-adjoint elliptic operators

自伴椭圆算子的解析差异的谱估计

• DOI: 10.48550/arxiv.1012.4596
• 发表时间: 2010
• 作者: Behrndt J

A remark on Schatten-von Neumann properties of resolvent differences of generalized Robin Laplacians on bounded domains

有界域上广义罗宾拉普拉斯算子求解差异的沙滕-冯·诺依曼性质的评述

• DOI: 10.48550/arxiv.0911.2443
• 发表时间: 2009
• 作者: Behrndt J

Direct and inverse spectral theorems for a class of canonical systems with two singular endpoints

一类具有两个奇异端点的正则系统的正谱定理和逆谱定理

• DOI: 10.48550/arxiv.1510.02635
• 发表时间: 2015
• 作者: Langer M

Indefinite Hamiltonian systems whose Titchmarsh-Weyl coefficients have no finite generalized poles of non-positive type

Titchmarsh-Weyl 系数不具有非正类型的有限广义极点的不定哈密顿系统

• DOI: 10.7153/oam-07-29
• 发表时间: 2013
• 期刊: Operators and Matrices
• 影响因子: 0.5
• 作者: Langer M

On the adjoint of a symmetric operator

关于对称算子的伴随

• DOI: 10.1112/jlms/jdq040
• 发表时间: 2010
• 期刊: Journal of the London Mathematical Society
• 作者: Behrndt J