摘要
本文给出分布余弦函数的定义 ,其中包括生成元为多值算子情形 ,并讨论退化性型分布余弦函数与退化型二阶 Cauchy问题、退化型积分余弦函数的关系 ,最后说明了非退化分布余弦函数的生成元亦生成正则余弦函数 .
In this paper we define distribution cosine functions covering the degenerate case. We also consider the degenerate distribution function generated by a multi valued operator A, its relation to the integrated cosine function and the wellposedness of the degenerate abstract Cauchy problem. We prove that A generates a distribution cosine function if and only if there is a k∈N∪{0} such that C k+1 (τ) is wellposed. Furthermore, we show that every generator of a nondegenerate distribution cosine function generates a regularized cosine function.
出处
《应用泛函分析学报》
CSCD
2002年第1期75-80,共6页
Acta Analysis Functionalis Applicata
基金
国家自然科学基金 (1 9971 0 3 1 )
