A generation result for cosine functions of operators (Q998925)

In this paper, the authors investigate the generation problem of cosine functions of linear operators. Suppose that \(A\) is closed and densely defined linear operator on a Banach space \(X\). Then the authors prove that for the abstract second order Cauchy problem, the equation has a unique weak solution for each pair \( x_0, x_1\in X \) if and only if \(A\) generates a strongly continuous cosine function of linear operators. As an application, they discuss the self-accessibility of the abstract second order system.