n次积分c余弦函数的Trotter-Kato逼近定理

The Trotter-Kato Approximation Theorems of N-times Integrated C Cosine Functions

n次积分余弦c函数是近年来提出并研究的一类算子族,它的逼近问题是研究的课题之一。目的在于研究如何用生成元预解式的逼近来刻画n次积分c余弦函数的Trotter-Kato逼近。利用Laplace变换得到了n次积分c余弦函数逼近的四个等价条件。当n=0时即为经典的c余弦函数相应的逼近结果。

N - times integrated c cosine function is a family of operators recently proposed. The approximation of n -times integrated e cosine functions is a subject studied by many researchers. This paper aims to get the approximation of n - times integrated e cosine functions by resolvents. The four equivalent conditions for approximations are obtained by means of Laplace transformations. In particular, the classical approximation of e cosine functions is the special case of our results for n = 0.