指数有界双参数C半群的逼近

Approximations for Exponentially Bounded Bi-Parameter C-Semigroups

基于C半群的定义,引入指数有界的双参数C半群的概念,借助于单参数C半群与双参数C半群之间的关系,利用范数与极限的一些性质,考察了指数有界的双参数C半群的逼近问题.从而对Banach空间中单参数C半群逼近定理及双参数强连续算子半群逼近定理进行了推广,为相应的抽象Cauchy问题提供了解决方案.

Based on the definition of C semigroups, a biparameter C semigroups with exponential boundedness is presented. By means of the relationships between one parameter Csemigroups and biparameter Csemigroups, with some properties about the norm and limit, some approximations are obtained for exponentially bounded biparameter Csemigroups, and then the approximation theorem of one parameter Csemigroups and strongly continuous biparameter semigroups on Banach space are generalized, and a kind of solution to its relative abstract Cauchy problems is thus provided.