有重谱的与多输入系统的分布参数系统的极点配置问题

极点配置问题是现代控制理论重要问题之一,其集中参数系统已有深入讨论,在分布参数系统里,则研究得远不够充分.资料[1]在假定算子A自伴,逆A~(-1)存在且是核算子的条件下,给出了单输入系统的极点配置问题的解答;     

D_()型算子的谱映射定理

本文是继在[1]、[2]中定义了型算子后着重讨论谱映射定理。它是线性算子谱理论中一条重要定理,在[3]、[4]、[5]、[6]中都作了讨论。我们感到企图在相当广泛的情况下获得这一定理可能是困难的。因此,我们从研究谱映射定理与谱超分布的某种延拓间的关系入手,对无界型算子的谱映射定理进行了讨论并获得了若干充分必要条件,使这一问题获得较圆满的解决。     

一类线性算子的一秩扰动与极点配置问题

线性系统理论关心的极点配置问题,实际即线性算子的谱扰动问题.我们研究了Banach 空间中一类线性离散算子的一秩扰动理论,相应得到极点配置问题的充要条件.§1.离散型算子的一秩扰动定义1.1.Banach 空间(?)中的线性算子 A 称为离散算子,如果在 A 的豫解集中有一λ,使豫解式 R(λ,A)=(λI-A)~(-1)为紧算子.下面的引理是熟知的.引理1.2.如果 A 是离散算子;那么,a)A 的谱集是可数点集,对每一λ(?)σ(A),R(λ,A)是紧算子.     

一类分布参数系统的极点配置问题

对于有穷维线性系统,极点配置的重要性是众所周知的,已经有比较完整的理论来处理这个问题.无穷维线性系统的极点配置,比起有穷维情形自然要复杂得多,这方面也有一些文章讨论(例如见[4,5,11]),但所得结果远远比不上有穷维情况.Hilbert 空间中的极点配置问题一般可叙述如下:设 H,U 为 Hilbert 空间 (H 称为状态空间,U 称为控制空间),A∶H→H 为线性(一般为闭稠定)算子,B∶U→H 为有界线性算子,我们用 σ(A)表示 A 的谱集,ρ(A) 表示 A 的预解集.问题在于寻找线性算子 K∶H→U,使得 σ(A+BK) 等于预先给定的复数集.这个问题显然与闭环控制系统     

(D)类线性算子的扰动问题

设 A∈U(X),当 V 满足什么条件时仍有 |A V∈U(X),即无条件基扰动问题.这是泛函分析研究的一个重要内容,它与微分方程中解的存在与稳定性紧密相连,以前的结果,大多数要求主算子 A——(D)类算子的谱具有相当强的分性离(1981年文[3]对 Hilbert 空间上的离散自共轭自算 A 给出了一个扰动结果,但文[10]已指出这个结果成立的充要条件是:A 还是(D)类算子).文[5]通过引入摄动有界泛函的概念,首先     

关于Cauchy问题唯一性的Nirenberg定理的一个推广

自 Nirenberg 在文[2]中推广了偏微分方程 Cauchy 问题的唯一性的 Calder(?)n 定理以后,许多文章都在文[2]的基础上,对算子的次主象征作某些限制后,进一步推广了 Nirenberg 的唯一性定理,得到许多好的结果。本文的推广从另一侧面进行,即对算子的次主象征不作任何限制,而是证明当算子的特征根虚部大于正数(?)时,其根的重数可不     

一类线性算子的一秩扰动

本文给出 l(?)-空间的理论,并利用这一理论处理(D)类算子一秩扰动问题,免去了对主算子 A 谱的分离性要求。     

参数边界条件下Sturm-Liouville算子的逆谱问题

本文研究参数边界条件下Sturm-Liouville算子的逆谱问题.利用Weyl函数的结果,证明对固定的n,n∈N_0,及不同的b_k,谱集合{λ_n(q,b_k)}_(k=1)~(+∞)能够唯一确定[0,1]上的势函数q(x),这个定理是文献[4]结果的本质推广.     

拟相似半控制算子的本质谱

讨论两个拟相似半控制算子的本质谱之间的关系,应用算子谱的精密结构的分析方法,给出拟相似半控制算子的本质谱相等的若干充分条件,所得结果改进和发展了L.R.W illiam s在文[7-8]中的有关结果.     

Hilbert空间中二阶广义分布参数系统的反馈控制与极点配置

应用泛函分析及算子理论方法讨论了Hilbert空间中二阶广义分布参数系统的反馈控制与极点配置问题,通过构造状态反馈的具体形式使所得闭环系统实现无限多个极点的配置;利用有界线性算子的广义逆给出了问题的解及解的构造性表达式;这对广义分布参数系统的极点配置研究具有重要的理论价值.     

C－半群的谱与其生成元谱之间的关系

本文首次给出了Ｃ－半群的预解集和谱的概念，得到了Ｃ－半群的谱与其生成元谱的一系列结果．     

双对称矩阵逆特征值问题解存在的条件

This paper discuss the following two problems:Problem I. Given . Find A,such thatAX=XA,where BSRn×n is the set of all n × n bisymmetric matrices.Problem II. Given Find A SE such that where SE is the solution set of Problem I,is the Frobenius norm.In this paper, the sufficient and necessary conditions under which SE is nonempty are obtained. The general form of SE has been given. Then expression of the solution A of Problem II is presented.     

Spectral decomposition of a matrix using the generalized sign matrix

An algorithm for spectral decomposition is presented which does not require knowledge of eigenvalues and eigenvectors. A set of eigenprojectors are defined which covers the entire spectrum of a matrix, and special attention is given to the projection on the zero eigenvalue. Some useful applications are discussed in the paper.     

Construction of full H-matrices with the given eigenvalues based on the Givens matrices

The inverse eigenvalue problem is about how to construct a desired matrix whose spectrum is the given number set. In this paper, in view of the Givens matrices, we prove that there exist three classes of full H-matrices which include strictly diagonally dominant full matrix, $\alpha$-strictly diagonally dominant full matrix and $\alpha$-double strictly diagonally dominant full matrix, and their spectrum are all the given number set. In addition, we design some numerical algorithms to explain how to construct the above-mentioned full H-matrices.     

非线性非自治系统的等度渐近稳定性

研究了非线性非自治系统平凡解的等度渐近稳定性。利用一个或两个Lyapunov函数得到了保证所给系统的平凡解等度渐近稳定性的几个充分判据,最后给出两个例子说明本文结果.     

On the inverse eigenvalue problem for nonnegative matrices of order two to five

In this paper, for a given set of numbers with special conditions, we construct a nonnegative matrix such that the given set is its spectrum.     

ON THE PARTIAL EQUIASYMPTOTIC STABILITY OF NONLINEAR TIME-VARYING DIFFERENTIAL EQUATIONS

In this paper, the problem of partial equiasymptotic stability for nonlinear time-varying differential equations are analyzed. A sufficient condition of partial stability and a set of sufficient conditions of partial equiasymptotic stability are given. Some of these conditions allow the derivative of Lyapunov function to be positive. Finally, several numerical examples are also given to illustrate the main results.     

SPECIAL AUTOMORPHISMS WITH CONTINUOUS SPECTRUM

Abstract

In this paper conditions are given for the primitive automorphism of a cyclic KS approximation to have continuous spectrum. If T: X → X admits a cyclic KS approximation with speed o(1/n) it is then shown that for a dense set of measurable sets A € 𝔉, T^A: X^A → X^A is weakly mixing, i.e. has continuous spectrum. In particular it is shown that if T_α is an irrational rotation on the unit circle there exists an uncountable dense set of measurable sets for which (T^α)^A has continuous spectrum.     

THE SPECTRUM OF CONTRACTIVE OPERATORS ON $\[{\pi _k}\]$

In this paper, it is shown that, for a contraction on $\[{\pi _k}\]$, the intersection of its spectrum with the exterior of the unit disk is a finite set of isolated eigenvalues, each of which has finite multplicity. Futhermore some relations between its spectrum and the spectrum of its minimal unitary dilation are established.     

Pre-compactness of isospectral sets for the neumann operator on planar domains

The Neumann operator maps the boundary value of a harmonic function tc its normal derivative. The inverse spectral properties of the Neumann operator associated to smooth, planar, Jordan curves are studied. The Riemann mapping theorem is used tc parametrize the set of planar Jordan curves by positive functions on the unit circle. By studying the zeta function associated to the spectrum, it is shown that isospectral sets of these functions are pre-compact in the topology of the L²-Sobolev space of order 5/2 - [euro]. Spectral criteria are given for the limiting curves of an isospectral set to be Jordan. A spectrally determined lower bound on the area of the interior of the curve is given.