α次积分C余弦算子函数的逼近定理

Approximation theorems of α-times integrated C cosine oprator functions

利用生成元预解式来刻画α次积分C余弦函数的Trotter-Kato逼近,给出α次积分余弦C函数的定义及基本性质,通过Laplace变换得到了α次积分C余弦函数逼近的4个等价条件,且当α为0时即为经典的C余弦函数相应的逼近结果。

The paper gives the definition and property of α-times integrated C cosine functions to get the approximation of α-times integrated C cosine functions by the approximation of generator and resolv- ents. The four equivalent conditions for approximations are obtained by means of Laplace transformations. In particular, the classical approximation of C cosine functions is the special case of our results for α=0.