1) bi-continuous C-semigroups
双连续C半群
1.
Based on the approximation theories of strong continuous semigroups on Banach space,and in combination with the concept of bi-continuous C-semigroups,the approximation theorems of bi-continuous C-semigroups is thus obtained by analyzing the relations between its generator and resolvent,and the said approximation theorem for the strong continuous semigroups on Banach space is then generalized.
基于Banach空间中强连续半群的逼近理论,结合双连续C半群概念,通过讨论其生成元与预解式之间的关系,得到双连续C半群的逼近定理,从而推广了Banach空间上强连续半群的逼近定理。
2) bi-continuous C-semigroup
双连续C-半群
1.
In this paper we investigate bi-continuous C-semigroups on Banach space X endowed with an additional locally convex topology τ.
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。
3) Bi-continuous n-times integrated C-semigroup
双连续n次积分C-半群
1.
Exponentially bounded bi-continuous n-times integrated C-semigroups and properties;
指数有界双连续n次积分C-半群及其性质
5) uniformly continuous C-semigroups
一致连续C半群
6) Strongly continuous bisemigroups
强连续双半群
补充资料：强连续半群
强连续半群
strongly-continuous son!-group
强连续半群[s枷叼y一c佣“nu0lls，”‘.9代阅.;c翻‘即“enpep曰.Ha，no月yrPynna] Banach空间X上具有以下性质的一族有界线性算子T(t)，r>0: l)T(t+;)x=T(r)T(:)x，r，了>0，x6X; 2)函数tl~T(t)x对任何x〔X在(O，的)上连续. 当1)成立时，所有函数tl一T(t)x(x‘X)的可测性，且特别地它们的单边(右或左)弱连续性，蕴涵T(t)的强连续性.对一个强连续半群，有限数 田一r叹r一’]n 11T(‘)1卜，纯‘一’In llT(r)11称为该半群的型(勿详of the semi一gouP).这样，函数t卜，T(t)x的范数在的的增长不快于指数e‘『.强连续半群的分类是基于当t，O时它们的性态.如果有一个有界算子J使得当t一，O时}T(t)一川}，O，则J是一个投影算子且T(t)=Je‘月，其中A是与J交换的一个有界线性算子.在这情形T(t)关于算子范数是连续的.如果J=I，则T(t)=c‘滩，一的
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