一类解析算子函数空间上的复合算子

本文用算子函数论的方法，研究了解析算子函数的Banach空间X，X0上的复合算子．给出此复合算子为有界的条件，并刻划了此复合算子在X0上为紧的特征．     

解析函数的Banach空间上之复合算子

本文研究了一类解析函数的Ｂａｎａｃｈ空间Ｘ上之复合算子，这类空间包含了Ｂｌｏｃｈ空间，并且可看作Ｂｅｒｇｍａｎ空间Ｌ１ａ（Ｄ）中具有原子分解的解析函数的对偶空间．我们刻划了这类空间上紧复合算子及Ｆｒｅｄｈｏｌｍ复合算子的特征，此外，还研究了具有闭值域的复合算子．     

冯·诺依曼代数的可测算子的性质

本文研究了冯·诺依曼代数的可测算子的基本性质,定义了阶梯算子,证明了任意一个正可测算子可以由阶梯算子在定义域内按照强算子拓扑逼近,从而证明了任意一个可测算子可以由投影在定义域内按照强算子拓扑逼近.此外,还讨论了可测算子与有界算子的复合算子的可测性.     

加权Bergman空间上的Toeplitz算子和Hankel算子

西方给出了Ｃ＾ｎ中单位球上的带权的Ｂｅｒｇｍａｎ空间上具一般符号的Ｔｏｅｐｌｉｔｚ算子和Ｈａｎｋｅｌ算子为紧的充要条件。     

模糊算子排序

完成了几种常用的模糊算子的排序工作.     

关于多个算子的Furuta型算子单调函数

设p≥1,且A、B是Hilbert空间上两个正算子,T.Furuta给出若A≥B>0,那么对任意t∈[0,1]有,G(r,s)=A-r/2{Ar/2(A-t/2BpA-t/2)sAr/2}1-t+r/(p-t)+srA-r/2是关于r,s在r≥t及s≥1上单调递减的,我们给出该结果可以推广到多个算子的情形.     

Hardy-Littlewood最大算子的两个推广

§1IntroductionHardy-Littlewood maximal operator has wide applications in many fields,such asquasiconformal analysis,partial differential equations(PDEs)and harmonic analysis.LetΩbe an open subset of Rn,the Hardy-Littlewood maximal operator is defined on Ll1oc(Ω)by the ruleMh(x)=MΩh(x)=sup∫-B(x,t)h(y)dy:0相似文献   

算子方程AX-XA=C的可解性

本文在一般Ｂａｎａｃｈ空间研究带无界算子Ａ的算子方程ＡＸ－ＸＡ＝Ｃ的可解性,利用单参数积分双半群方法,通过在算子代数Ｌ（Ｅ）上考虑间断问题弱解,证明了当算子Ａ在Ｌ（Ｅ）上诱导的算子Ａ是弱积分双半群的母元时,只要Ｃ满足一定条件,上述算子方程可解．     

SOME PROPERTIES OF INTEGRATED BISEMIGROUPS

1 IntroductionRecently tl1e collcept of integrated bisen1group is developed fOr solving the abstract dy-nantic equatioll in [1]. This is an extellsioll of theory of bisemigroup8I2--4t1o-l5] alld integratedsentigroups[5-9]. In tl1e present paper, we will discuss the properties of integrated bisen1igroups.First we recall sollle basic properties of integrated bisentigroups, including the definition andthe infillitesimal generator of illtegrated bisemigroups. In Section 3, we discuss the structu…     

线性算子双半群的扰动定理

本文研究有界线性算子强连续双半群的扰动问题。文中首先研究与强连续双半群母元有关的算子方程的可解性与算子的相似性。在此基础上证明了在一定条件下可化为指数衰减的强连续双半群经适当扰动后仍是一个可化为指数衰减的强连续双半群。     

积分双半群与抽象动力方程的可解性

本文从一类抽象积分微分方程的可解性，引人积分双半群的概念，并讨论了积分双半群的一些性质．利用积分双半群，说明了一类抽象动力方程的可解性，特别是抽象动力方程边值问题的可解性．     

Banach空间积分双半群的生成条件

研究Banach空间中积分双半群的生成条件.利用算子A的豫解算子,给出了积分双半群T(t)的生成定理.结果表明:如果对任意的x∈X,f∈X*,以及A|λ]<δ,λ∈ρ(A),有∈Lp(R),则存在算子族S(t),t∈R,S(t)强连续且满足积分双半群的定义.     

强连续双半群与积分双半群

本文研究积分双半群与有界线性算子双半群的关系,证明了Ｂａｎａｃｈ空间Ｘ上的指数有界积分双半群可以作为Ｘ的某个子空间上具有较强范数拓扑下的有界线性算了强连续双半 积分双半群也可作为较大空间上俱有较弱范数拓扑下的有界线性算子强连续双半群积分的限制,上述结果可以用来解释抽象边值问题的弱解的意义。     

Necessary conditions of nondominated solutions in multicriteria decision making

A partial integrodifferential equation is studied in which the derivatives of highest order also contain a discrete and a distributed delay. By means of abstract regularity results, global existence and uniqueness of a strict solution are obtained; moreover a characterization of the infinitesimal generator of the solution operator is given.     

Backward stochastic differential equations on manifolds

The problem of finding a martingale on a manifold with a fixed random terminal value can be solved by considering BSDEs with a generator with quadratic growth. We study here a generalization of these equations and we give uniqueness and existence results in two different frameworks, using differential geometry tools. Applications to PDEs are given, including a certain class of Dirichlet problems on manifolds.     

Stochastic functional differential equations modelling materials with selective recall

We study a problem in stochastic functional differential equations which, in addition to a standard one-one-parameter noise term involves a random perturbation of the memory. This problem can also be regarded as a first order hyperbolic system of stochastic partial differential equations with given initial data and nonlocal boundary data. Existence and uniqueness of a solution is established and the generator of the associated Markov process is analyzed. Thereafter, for two model problems arising from first- and second-order integro-differential equations suggested by physical applications we establish asymptotic stability in probability of the associated stochastic processes.     

BSDEs with two RCLL reflecting obstacles driven by Brownian motion and Poisson measure and a related mixed zero-sum game

In this paper we study Backward Stochastic Differential Equations with two reflecting right continuous with left limit obstacles (or barriers) when the noise is given by Brownian motion and a mutually independent Poisson random measure. The jumps of the obstacle processes could be either predictable or inaccessible. We show the existence and uniqueness of the solution when the barriers are completely separated and the generator uniformly Lipschitz. We do not assume the existence of a difference of supermartingales between the obstacles. As an application, we show that the related mixed zero-sum differential–integral game problem has a value.