L2[α,∞)上高阶Sturm-Liouville算子下半有界性与谱

采用泛函分析与不等式渐近估计的方法,根据微分算子系数的特点,研究了高阶Sturm-Liouville微分算子下半有界性并得到其为下半有界的一些判定准则,同时给出了其下界的估计.这些结果对研究微分算子的谱是有益的.     

一类具指数系数的对称微分算子谱的离散性

研究了具指数函数系数的2n阶实系数微分算式生成的对称微分算子,利用算子的直和分解法及不等式估计得到此类微分算子谱是离散的充分条件.     

学习理论中核函数逼近的Jackson型不等式（英文）

从微分算子角度理解核函数空间,借助经典Fourier变换研究核函数逼近问题.应用Fourier乘子算子和算子半群定义了一种光滑模,证明其与一种基于微分算子的K-泛函的等价性,由此给出了刻画核函数逼近收敛性的Jackson不等式.进一步证明,如果微分算子为Riesz势算子或Bessel势算子,逼近的收敛性可以转化为卷积算子逼近.特别地,给出了再生核Hilbert空间逼近的一种上界估计.     

Banach空间中一类二元算子方程的可解性及应用

在新的初始条件下,利用锥理论和半序方法,研究了Banach空间中二元算子方程A(x,y)=Lx的迭代求解问题.在对算子A和L的连续性和紧性不做任何假定的情况下,证明了其解的存在性和唯一性.还证明了本文所构建的迭代序列收敛于该解,估计了其收敛速度.最后将所获结果用于讨论一类微分-积分方程解的存在性问题.     

一类具欧指积系数微分算子谱的离散性(英文)

利用算子直和分解的方法和二次型估计的方法,研究了一类具欧指积系数微分算子谱的离散性,得到了其谱是离散的一些充分条件.     

高阶加权微分算子谱的离散性

本文研究了加权的高阶微分算子的谱. 利用分解的方法和不等式的估计, 得到了一些高阶对称微分算子的任何自共轭扩张的谱离散的充分条件, 推广了 Pfeiffer , Sun, Glazman 等人的结果,利用这些结果可以判别某些微分算子谱的离散性.     

两类单边算子的半连续性研究

本文研究了单边Hardy-Littlewood极小算子的上半连续性及单边Hardy-Littlewood极大算子的下半连续性问题.利用半连续性的相关性质和新型集合测度估计等获得了单边Hardy-Littlewood极小算子m~+f(x)在R~n上的上半连续性和单边Hardy-Littlewood极大算子M~+f(x)在R~n上的下半连续性,推广了Hardy-Littlewood极大算子的半连续性成果.     

四阶不定微分算子非实特征值的界

给出了四阶正则不定微分算子仅在可积条件下的非实特征值上界和下界的估计.更一般地,非实特征值的下界可以利用Krein空间的自共轭算子得到.     

依赖时间的发展方程Galerkin解的敛速估计

黄明游和Vidav Thomee,P.H.Sammon研究了当A=L_1+L_2是二阶微分算子,其主部L_1是正定对称时,依赖时间的非自伴抛物方程,给出了半离散Galerkin解及其关于时间的导数的L~2(Ω)-模误差估计。我们考虑的是如下形式的发展方程     

一类热弹性板的空间衰减估计

研究了二维空间中半无限带形区域上一类含有双调和算子的热弹性系统板解的空间性质.首先构造一个能量表达式,然后利用微分不等式技术,推导出该能量表达式是可由它本身的一阶导数控制的微分不等式,最后得到解的空间衰减估计.该结果可看成是Saint-Venant原则在双曲抛物耦合双调和方程组上的应用.     

Differential properties of the Dirichlet-Neumann operator

Under consideration is the Dirichlet-Neumann operator on the boundary of the distorted half-space bounded below by a surface which is close to a hyperplane. We establish the differential properties of the operator depending on the smoothness of the boundary and find an expression for it.     

Self-conjugacy of abstract differential operators of the hyperbolic type

Sufficient conditions are obtained for the self-conjugacy of certain operators generated on a semiaxis or a complete axis by a differential expression of the form l[y]=y+Ay–q(t)y, where A is a self-conjugate operator bounded below in a separable Hilbert space H, and, for almost all t, q(t) is a bounded self-conjugate operator in H, locally summable with the square of the norm.Translated from Matematicheskie Zametki, Vol. 20, No. 5, pp. 703–708, November, 1976.     

Remarks on virtual bound states for semi—bounded operators

We calculate the number of bound states appearing below the spectrum of a semi—bounded operator in the case of a weak, indefinite perturbation. The abstract result generalizes the Birman—Schwinger principle to this case. We discuss a number of examples, in particular higher order differential operators, critical Schrodinger operators, systems of second order differential operators, Schrodinger type operators with magnetic fields and the Two—dimensional Pauli operator with a localized magnetic field.     

On the conditions of solvability and the resolvent of a second-order deferential boundary operator in a space of vector functions

A boundary differential operator generated by the Sturm-Liouville differential expression with bounded operator potential and nonlocal boundary conditions is considered. The conditions for a considered operator to be a Fredholm and solvable operator are established and its resolvent is constructed.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 4, pp. 517–524, April, 1995.     

Sliding Mode Techniques for Robust Trajectory Tracking as well as State and Parameter Estimation

Practical applications are often affected by uncertainties—more precisely bounded and stochastic disturbances. These have to be considered in robust control procedures to prevent a system from being unstable. Common sliding mode control strategies are often not able to cope with the mentioned impacts simultaneously, because they assume that the considered system is only affected by matched uncertainty. Another problem is the offline computation of the switching amplitude. Under these assumptions, important nonlinear system properties cannot be taken into account within the mathematical model of the system. Therefore, this paper presents sliding mode techniques, that on the one hand are able to consider bounded as well as stochastic uncertainties simultaneously, and on the other hand are not limited to the matched case. Firstly, a sliding mode control procedure taking into account both classes of uncertainty is shown. Additionally, a sliding mode observer for the simultaneous estimation of non-measurable system states and uncertain but bounded parameters is described despite stochastic disturbances. This is possible by using intervals for states and parameters in the resulting stochastic differential equations. Therefore, the Itô differential operator is involved and the system’s stability can be verified despite uncertainties and disturbances for both control and observer procedures. This operator is used for the online computation of the variable structure part gain (matrix of switching amplitudes) which is advantageous in contrast to common sliding mode procedures.     

Boundedness from below of composition operators on the Bloch spaces

This paper proves that a necessary condition for a composition operator on the Bloch space of the unit disk to be bounded below given by Ghatage, Yan and Zheng is also sufficient. Given furthermore are a sufficient condition and a necessary condition of the boundedness from below for a composition operator on the Bloch space of a unit ball with dimensions bigger than one.     

W_2~m空间中样条插值算子与最佳逼近算子的一致性

This paper discusses generalized interpolating splines which determined by n order linear differential operators, and the best operators of interpolating approximation in W_2~m spaces, The explicit constructive method for the reproducing kernel in W_2~m space is presented, and proves the uniformity of spline interpolating operators and the best operators of interpolating approximation W_2~m space by reproducing kernel. The explicit expression of approximation error on a bounded ball in W_2~m space, and error estimation of spline operator of approximation are obtained.     

W_2~m空间中样条插值算子与最佳逼近算子的一致性

由线性微分算子确定的样条是连接多项式样条与希氏空间中抽象算子样条的重要环节,对微分算子样条的研究,既可从更高的观点揭示和概括多项式样条,又可启示我们去发现抽象算子样条的一些新的理论和应用． Ｇｒｅｅｎ函数是研究微分算子样条的重要工具 ［１］,但在微分算子插值样条的计算及将样条用于数值分析中,再生核方法起着更重要的作用．文献［２］［３］给出了与二阶线性微分算子插值样条有关的再生核解析表达式;由此得到了二阶微分算子插值样条与空间Ｗ_２～１［ａ,ｂ］中最佳插值逼近算子的一致性;而且还利用再生核给出了Ｈｉ…     

$\mathbb{C}^{n}$中$\mu$-Bergman空间的刻画和微分复合算子

设$p>0$, $\mu$和$\mu_{1}$是$[0,1)$上的正规函数. 本文首先给出了$\mathbb{C}^{n}$中单位球上$\mu$-Bergman空间$A^{p}(\mu)$的几种等价刻画; 然后 分别刻画了$A^{p}(\mu)$到$A^{p}(\mu_{1})$的 微分复合算子$D_{\varphi}$为有界算子以及紧算子的充要条件, 同时给出了当$p>1$时$D_{\varphi}$为 $A^{p}(\mu)$到$A^{p}(\mu_{1})$上紧算子的一种简捷充分条件和必要条件.     

$2\times 2$阶上三角算子矩阵的谱扰动

研究了Hilbert空间H(?)K上的2×2阶上三角算子矩阵Mc=(AO CB)当A,B 给定,C为任意有界线性算子时,对Mc的点谱、剩余谱、连续谱的扰动分别给出了描述．