无穷维Hamilton算子的可逆性及其应用

本文研究了无穷维Hamilton算子的可逆性问题,进而,刻画了无穷维Hamilton算子的谱的分布,并运用内部的逆紧性描述了无穷维Hamilton算子的逆紧性.最后,给出了无穷维Hamilton算子的可逆性问题在Dirac算子的可逆性问题中的应用.     

闭值域稠定闭算子的Moore-Penrose广义逆的有限维逼近

研究了闭值域稠定闭算子的Moore-Penrose广义逆的有限维逼近问题.由于可接受条件相当强,我们提出更弱的条件P_(G(T_n))■P_(G(T))来研究稠定闭算子MoorePenrose广义逆的有限维逼近,也能得到相同的结论.特别地,当T为有界算子且T_n=Q_nTP_n时,条件P_(G(T_n))■P_(G(T))自然成立,于是有界线性算子Moore-Penrose广义逆的有限维逼近的一些结果会成为定理3.3的推论.     

Banach空间中线性算子的齐性广义逆

本文首先在Banach空间内引进拟线性投影算子的概念,由此给出Banach空 间内线性算子的齐性广义逆的统一定义。齐性广义逆包含线性广义逆、单值度量广义 逆.本文证得齐性广义逆存在的充分必要条件.     

Banach空间中线性算子核逆的一致有界性与收敛性（英文）

本文主要研究Banach空间中线性算子核逆的一致有界性与收敛性之间的关系.首先证明核逆的一致有界性与收敛性的等价性,给出了核逆的表达式.其次,利用稳定扰动,证明核逆的稳定扰动与连续性是等价的.作为应用,我们还给出有限秩算子核逆的连续性特征,并给出扰动算子的核逆具有最简表达式的充分必要条件.     

Banach空间中集值度量广义逆齐性单值选择的判据

本文研究了Banach空间(X,‖·‖),(Y,‖·‖)上具有闭值域的稠定闭算子T:X→Y的(集值)度量广义逆.在限定X为自反的、Y为一般的Banach空间且算子值域R(T)为空间Y中Chebyshev子空间时,证明了算子T具有非空闭凸集值的度量广义逆的存在性,运用Banach空间中广义正交分解定理,得出算子T的集值度量广义逆具有唯一齐性单值选择,并且该单值选择恰为赋等价严格凸范数的空间Xr=(X,‖·‖_r)上算子T的Moore-Penrose度量广义逆.特别地,将抽象的Banach空间X与Y具体化为有限维Banach空间l₁ⁿ=(Rn,‖·‖₁)(即n维空间Rn赋l₁范数)与有限维Hilbert空间(即m维欧式空间l₂^m=(Rm,‖·‖₂),亦即m维空间赋l₂范数),线性算子T可具体表示为m×n阶矩阵A,得到了从n维空间l₁ⁿ到m维空间l     

2×2算子矩阵的逆

设H和K为复的无限维可分Hilbert空间．本文利用算子的几何结构着重研究了Hilbert空间H(?)K上的2×2算子矩阵的逆,给出了一些有意义的结果．     

广义投影和超广义投影的一些等价刻画

利用算子矩阵分块技巧和算子的广义逆,研究了复Hilbert空间上广义投影和超广义投影算子的性质,给出了它们的一些等价刻画.     

正线性算子的Young型逆不等式的一个改进

本文研究了正线性算子的Young型逆不等式的问题.利用算子单调函数以及凸函数的性质,获得了若干带有Kantorovich常数的Young型逆不等式标量形式及相对应的正线性算子的Young型逆不等式的改进形式,推广了现有文献中的结论.     

正线性算子的Young型逆不等式的一个改进（英文）

本文研究了正线性算子的Young型逆不等式的问题.利用算子单调函数以及凸函数的性质,获得了若干带有Kantorovich常数的Young型逆不等式标量形式及相对应的正线性算子的Young型逆不等式的改进形式,推广了现有文献中的结论.     

任意除环上矩阵的广义逆

该文使用投影算子方法研究任意除环上矩阵的广义逆, 建立了具有指定值域和零空间的{2} 逆的刻划和表示理论. 作为应用, 获得了带有对合函数的Moore Penrose逆, 群逆和Dra zin逆的一些新的表式.     

A Parametrization of the Irreducible Representations of a Compact Inverse Semigroup

The aim in this article is to provide a parametrization of the finite dimensional irreducible representations of a compact inverse semigroup in terms of the irreducible representations of maximal subgroups and order theoretic properties of the idempotent set. As a consequence, we obtain a new, and more conceptual, proof of the following theorem of Shneperman: a compact inverse semigroup has enough finite dimensional irreducible representations to separate points if and only if its idempotent set is totally disconnected. Moreover, we also prove that every norm continuous irreducible *-representation of a compact inverse semigroup on a Hilbert space is finite dimensional.     

一类微分方程特解的逆矩阵求法

根据函数求导运算与函数的不定积分互为逆运算的思想,以及有限维函数向量空间在求导运算下不变的条件,利用逆矩阵方法得到向量空间中基函数的不定积分,从而给出一定条件下用逆矩阵法求一类常系数非齐次线性微分方程特解的新方法.     

Applications of Inverse Limits to Extensions of Operators and Approximation of Lipschitz Functions

We consider extensions of linear operators from finite dimensional subspaces. As a corollary of Steenrod's theorem about inverse limits of topological spaces, we obtain new results concerning approximation in tensor product spaces and the stability of the Cauchy functional equation.     

Determination of the Robin coefficient in a nonlinear boundary condition for a steady‐state problem

In this paper, a constant heat transfer coefficient present in a nonlinear Robin‐type boundary condition associated with an elliptic equation is reconstructed uniquely from a single boundary energy measurement. Two types of such boundary energy measurement are considered, and solvability theorems for the solution of the resulting nonlinear inverse problems are provided. Further, one‐dimensional numerical results are presented and discussed. Copyright © 2008 John Wiley & Sons, Ltd.     

The recovery of the acoustic stiffness coefficient

We are concerned with the reconstruction of a non‐differentiable acoustic stiffness reactance coefficient of a one‐dimensional hyperbolic equation using the smallest possible number of boundary readings generated by classical initial conditions. To this end, a complete set of spectral data of a string is extracted from either a single or at most two readings of the trace of the solution on the boundary. The sought coefficient is then uniquely recovered by the Krein inverse spectral theory. Copyright © 2013 John Wiley & Sons, Ltd.     

A robust method for new fractional hybrid chaos synchronization

In this paper, a robust mathematical method is proposed to study a new hybrid synchronization type, which is a combining generalized synchronization and inverse generalized synchronization. The method is based on Laplace transformation, Lyapunov stability theory of integer‐order systems and stability theory of linear fractional systems. Sufficient conditions are derived to demonstrate the coexistence of generalized synchronization and inverse generalized synchronization between different dimensional incommensurate fractional chaotic systems. Numerical test of the method is used. Copyright © 2016 John Wiley & Sons, Ltd.     

Hartwig’s triple reverse order law revisited

We extend the classical Hartwig’s triple reverse-order law for the Moore–Penrose inverse to closed range bounded linear operators on infinite dimensional Hilbert spaces.     

Determination of a time‐ and space‐dependent heat flux relaxation function by means of a restricted Dirichlet‐to‐Neumann operator

We consider an inverse problem to recover a space‐ and time‐dependent relaxation function of heat flux in a three‐dimensional body on the basis of the restriction of the Dirichlet‐to‐Neumann operator of the related equation of heat flow onto a set of Dirichlet data of the form of a product of a fixed time‐dependent coefficient and a free space‐dependent function. Uniqueness of the solution of this inverse problem is proved. Copyright © 2004 John Wiley & Sons, Ltd.     

Representations and properties of the W-Weighted Drazin inverse

Several new representations of the W-weighted Drazin inverse are introduced. These representations are expressed in terms of various matrix powers as well as in terms of matrix products involving the Moore–Penrose inverse and the usual matrix inverse. Also, the properties of various generalized inverses which arise from derived representations are investigated. The computational complexity and efficiency of the proposed representations are considered. Representations are tested and compared among themselves in a substantial number of randomly generated test examples.