a次积分C-半群的扰动

在α次积分半群的扰动理论的基础上,讨论了α次积分C-半群的可交换扰动问题,得到了α次积分D半群的扰动定理.     

指数有界双连续α次积分C半群的扰动

在α次积分C半群和双连续n次积分C半群的基础上,探讨了双连续α次积分C半群的扰动性,得到了双连续α次积分C半群的扰动定理,并且在局部Lipschitz连续条件下证明双连续α次积分C半群的扰动理论仍然成立.     

关于n次积分C半群的扰动

研究了n次积分C半群的可交换扰动问题,得到其扰动定理;并根据n次积分C半群与C半群的关系得到了n次积分C半群的两个乘积扰动定理.     

带非稠定生成元的指数有界C半群与积分半群Ⅱ：扰动

本文研究指数有界C半群在C不必具有稠值域时的扰动问题。同时也得到n次积分半群带非稠定生成元时的扰动结果。改进与发展了Tanaka、Neuberander、Kellermann和Hieber以及作者之一的相应工作。 C半群、积分半群、非稠定生成元、扰动。     

Markov积分半群的扰动和逼近

为了研究Markov积分半群的扰动和逼近,根据转移函数与Markov积分半群之间一一对应关系,以及转移函数的扰动和逼近,通过积分的方法,获得了Markov积分半群的广义Phillips扰动定理和Trotter-Kato逼近定理.     

T(t)积分半群

本文引入Ｔ（ｔ）积分半群的概念，它是ｎ次积分半群［１］及α次积分半群［２］的推广．我们给出Ｔ（ｔ）积分半群的定义、生成定理，并讨论相应的一类积分型抽象Ｃａｕｃｈｙ问题解的存在唯一性．     

α-次积分C-半群与抽象柯西问题

本文引入一般的α-次积分C-半群和mildα-次积分C-存在族概念,并讨论它们与抽象柯西问题的联系．     

α—次积分C—半群与抽象栖西问题

本文引入一般的α－次积分Ｃ－半群和ｍｉｌｄａα－次积分Ｃ－存在族概念,并讨论了它们与抽象柯西问题的联系。     

α次积分余弦函数

该文研究了α次积分余弦函数的一些基本问题．目的是证明α次积分余弦函数的一些基本性质、生成定理、与α次积分半群的关系等．获得的结果改进和统一了由Arendt和Kellermann、Li和Shaw、Zheng等给出的相应结论．     

指数有界双参数n阶m次积分C群的指数公式

利用经典算子半群理论中的方法,基于指数有界双参数n阶α次积分C群的概念,得到了指数有界双参数n阶m次积分C群的指数公式     

Differential and Analytical Properties of Semigroups of Operators

We systematically analyze differential and analytical properties of various kinds of semigroups of linear operators, including (local) convoluted C-semigroups and ultradistribution semigroups. The study of differentiable integrated semigroups leans heavily on the unification of the approaches of Barbu (Ann Scuola Norm Sup Pisa 23:413–429, 1969) and Pazy (Semigroups of linear operators and applications to partial differential equations. Springer, Berlin, 1983). We furnish illustrative examples of operators which generate differentiable integrated semigroups, further analyze the analytic properties of solutions of the backwards heat equation, and prove that several introduced classes of differentiable semigroups persist under bounded ‘commuting’ perturbations.     

A class of semigroups regularized in space and time

We consider α-times integrated C-regularized semigroups, which are a hybrid between semigroups regularized in space (C-semigroups) and integrated semigroups regularized in time. We study the basic properties of these objects, also in absence of exponential boundedness. We discuss their generators and establish an equivalence theorem between existence of integrated regularized semigroups and well-posedness of certain Cauchy problems. We investigate the effect of smoothing regularized semigroups by fractional integration.     

α-次积分半群的Trotter-kato定理

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＷｈｅｎｗｅｉｎｔｅｇｒａｔｅｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ，ｗｅｃａｎｆｏｒｍｕｌａｔｅｍａｎｙｏｆｔｈｅｍａｓａｎａｂｓｔｒａｃｔＣａｕｃｈｙｐｒｏｂｌｅｍ．ＡｎａｔｕｒａｌｑｕｅｓｔｉｏｎｉｎｔｈｅｔｈｅｏｒｙｉｓｔｏｆｉｎｄｓｕｉｔａｂｌｅｃｏｎｄｉｔｉｏｎｓｕｎｄｅｒｗｈｉｃｈａｓｅｑｕｅｎｃｅｏｆａａｂｓｔｒａｃｔＣａｕｃｈｙｐｒｏｂｌｅｍ．ｕ′ｎ＝Ａｎｕｎ（ｔ），ｕｎ（０）＝ｘｎ，ｆｏｒｔ≥０，ｎ＝１，２，…ｉｎａｎａｒｂｔｉｒａｒｙＢａ…     

积分半群的Lumer—Phillips定理

一个n次积分半群S(t)如果满足‖S^(n)(t)x‖≤‖x‖,A↓t≥0,x∈D(A^n),我们就称S(t)是一压缩的n次积分半群,其中A为半群S（t)的生成元。在本中,我们完全刻划了n次压缩积分半群的特征,给出了n次压缩积分半群的Lumer-Phillips定理。     

Quasi-C-Ehresmann Semigroups and Their Subclasses

We introduce the concept of a quasi-C-Ehresmann semigroup. Some special quasi-C-Ehresmann semigroups will be considered. We will show that the quasi-C-Ehresmann semigroups are special U-semiabundant semigroups and orthodox U-liberal semigroups, which have been recently studied by several authors. Some characterization theorems of this new class of semigroups are obtained. Many results of quasi-C-semigroups in the literature can be extended to quasi-C-Ehresmann Semigroups.     

Cone-transitive matrix semigroups

Semigroups of matrices (over an ordered field) with non-negative entries are considered. A complete characterization is obtained for the semigroups which are minimal transitive on the positive (or non-negative) cone of the underlying vector space. Consequently, an explicit form for the semigroups sharply transitive on the cone is derived.     

The lattice of semigroup varieties

Semigroups are considered here in terms of the identities which they may satisfy with the emphasis on the identities and on classes of semigroups defined by identities, rather than on the semigroups themselves. These classes, called varieties, form a lattice under inclusion and it is illuminating to interpret properties of semigroup identities and varieties in terms of this lattice, its cardinality, its atoms, its infinite chains, and so on. This paper is an expansion of addresses to the Southeastern Section of the Mathematical Association of America at East Carolina University, March 1968 and to the Symposium on Semigroups and Rings at the University of Puerto Rico, Mayaguez, March 1970. The preparation of the paper was supported in part by NSF Grants GP 6597 and GP 20638.     

矩形拟正则半群及矩形群的半直积和圈积

给出了两个半群的半直积和圈积为矩形拟正则半群和矩形群的充要条件。     

The equivalence of uniquely divisible semigroups and uniquely representable semigroups on the two-cell

This talk brings together the results of several papers in order to show that the uniquely divisible semigroups on the two-cell are exactly the uniquely representable semigroups on the two-cell. From an address delivered at the Second Florida Symposium on Automata and Semigroups at the University of Florida, 1971.