International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 575-580
doi:10.1155/S0161171296000798
Integrated cosine functions
Quan Zheng
Dept. of Math., Huazhog Univ. of Science and Technology, Wuhan 430074, China
Abstract
In order to the second order Cauchy problem (CP2):x″(t)=Ax(t), x(0)=x∈D(An), x″(0)=y∈D(Am) on a Banach space, Arendt and Kellermann recently introduced the integrated cosine function. This paper is concerned with its basic theory, which contain some properties, perturbation and approximation theorems, the relationship to analytic integrated semigroups, interpolation and extrapolation theorems.