双参数有界算子C群的生成定理

Generation theorem of two parameter bounded operator Cgroups

在Banach空间上,根据双参数C半群的无穷小生成元与C群的性质,提出双参数有界算子C群的无穷小生成元是双参数有界线性算子在(0,0)处的全微分与C-1的积。定理1证明双参数有界算子C群的无穷小生成元的性质;定理2根据双参数有界算子C群的无穷小生成元的性质,提出线性变换是双参数有界算子C群的无穷小生成元的充要条件,即双参数有界算子C群的生成定理,并且给予证明。最后,总结双参数有界算子C群的性质,并且研究双参数有界算子C群有利于双参数C半群以及算子半群等在C群方向的进一步研究。

According to the property of the infinitesimal generator of two parameter Csemigroups and Cgroups in the Banach Space,it is introduced that the infinitesimal generator of two parameter bounded operator C groups is the multiplication of the total differential of two parameter bounded operator at（0,0）and C-1.It proves the property of the infinitesimal generator of two parameter bounded operator Cgroups in the theorem one.Then,according to the property of the infinitesimal generator of two parameter bounded operator Cgroups,that linear transformation is the necessary and sufficient condition of the infinitesimal generator of two parameter bounded operator C groups,namely the generation theorem of two parameter bounded operator Cgroups,is obtained in the theorem two.Finally,it is summarized that the property of two parameter bounded operator Cgroups.And the study of two parameter bounded operator Cgroups is favorable for the further study of two parameter Csemigroups and Cgroups.