Integrated cosine functions - Quan Zheng (International Journal of Mathematics and Mathematical Sciences)
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.