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。     

双连续n次积分C余弦函数的逼近定理

基于双连续半群概念,引入一致双连续半群序列概念,借助Laplace变换和Trotter-Kato定理,考察双连续n次积分C余弦函数与C-预解式之间的关系,得到逼近定理的稳定性条件,进而得出双连续n次积分C余弦函数逼近定理.从而对Banach空间强连续半群逼近定理和双连续半群逼近定理进行了推广,为相应抽象的Cauchy问题提供了解决方案.     

广义算子半群的遍历及概率逼近定理

首先给出了广义算子半群的Abel-遍历和Cesaro-遍历的定义,对两种遍历的性质进行了刻画,研究了两种遍历的等价条件.其次,利用Pettis积分、算子值数学期望及广义连续修正模等工具给出广义算子半群的概率逼近表达式.     

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。     

双连续N次积分C-半群的逼近定理

在C0半群和双连续半群逼近定理的启发下,讨论了双连续n次积分C-半群的逼近定理.     

C半群的概率逼近问题

借助Pettis积分、随机过程、矩生成函数及算子值数学期望,给出了一般形式的C半群概率逼近指数公式、生成定理及其收敛速度的估计式,也从另一个角度得出C半群概率表示的Vonorovskaya型渐近公式.     

局部有界的双连续C-半群及其逼近定理

本文研究了在带有一个局部凸拓扑τ的Banach空间X上双连续C-半群,结合双连续半群和C-半群的逼近定理,得到了双连续C-半群的逼近定理.     

C-半群与C_0—半群的关系

在这篇文章中证明了C-半群在限制空间中为C_0-半群,首次讨论了C-半群的解析性     

C半群概率表示的局部饱和性

本文应用经典的Ｆｅｌｌｅｒ－Ｔｈｏｔｔｅｒ型算子在Ｃω［０，＋∞］空间中局部小ｏ饱和定理，建立Ｂａｎａｃｈ空间上Ｃ半群概率表示的局部小ｏ饱和定理．     

局部紧拓扑半群上概率测度卷积幂的若干极限定理

我们通过研究极限测度的不变性质，讨论了局部紧拓扑半群上概率测度卷积幂的若干极限性状．推广了[1]－[3]中的若干结果．     

Asymptotic Formula for Probabilistic Representations of （C_0） Operator Semigroups

ＡｓｙｍｐｔｏｔｉｃＦｏｒｍｕｌａｆｏｒＰｒｏｂａｂｉｌｉｓｔｉｃＲｅｐｒｅｓｅｎｔａｔｉｏｎｓｏｆ（Ｃ_０）ＯｐｅｒａｔｏｒＳｅｍｉｇｒｏｕｐｓ￥ＣｈｅｎＷｅｎｚｈｏｎｇ（陈文忠）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉａｍｅｎＵｎｉ?..     

Topologically Complete Representations of Inverse Semigroups

A representation of an inverse semigroup by means of partial open homeomorphisms of a topological T ₀ -space is called topologically complete if the domains of these partial homeomorphisms form a base of the topology. It is shown how to construct topologically complete representations on the base of a ternary relation satisfying some elementary axioms. This result makes it possible to obtain a pseudo-elementary axiomatization for inverse semigroups that have faithful topologically complete representations in T ₁ ,T ₂ and T ₃ -spaces. A topology is introduced on any antigroup; this topology is a concomitant of the algebraic structure and every topologically complete representation is continuous with respect to this topology.     

A Perron-Frobenius-type Theorem for Positive Matrix Semigroups

One consequence of the Perron–Frobenius Theorem on indecomposable positive matrices is that whenever an \(n\times n\) matrix A dominates a non-singular positive matrix, there is an integer k dividing n such that, after a permutation of basis, A is block-monomial with \(k\times k\) blocks. Furthermore, for suitably large exponents, the nonzero blocks of \(A^m\) are strictly positive. We present an extension of this result for indecomposable semigroups of positive matrices.     

A Uniform Ergodic Theorem for Commuting Semigroups

The existence of the limit, in the uniform topology, of theaverages of a finite family of commuting strongly continuoussemigroups of bounded linear operators in a Banach space ischaracterised in terms of infinitesimal generators.     

A Decomposition Theorem for Group Representations

In this paper we establish a decomposition theorem for an ordinary representation of a finite group G in any category C{\mathcal C} which expresses a suitable irreducible representation of G as the tensor product of two projective ones. The celebrated theorem due to Clifford for a linear representation turns out to be a particular case of it. For that purpose, a definition of projective extension of an ordinary representation of a normal subgroup of G is introduced, as well as a tensor product between two of them.     

Extensions of Isometric Dual Representations of Semigroups

Let T be a dual representation of a suitable subsemigroup Sof a locally compact abelian group G by isometries on a dualBanach space X=(X_*)^*. It is shown that (X, T) can be extendedto a dual representation of G on a dual Banach space Y containingX, and that this extension can be done in a canonical way. Inthe case of a representation by *-monomorphisms of a von Neumannalgebra, the extension is a representation of G by *-automorphismsof a von Neumann algebra.     

广义算子半群的扰动定理

算子扰动问题是研究微分方程的一个重要工具,首先结合Hilbert空间中有界算子引导的广义算子半群的定义研究了广义半群的性质;其次重点讨论了广义算子半群的扰动问题,给出了广义算子半群的加法扰动定理成立的条件.