If A is the generator of an exponentially bounded C-cosine function on a Banach space X, then the abstract Cauchy problem (ACP) for A has a unique solution for every pair (x, y) of initial values from (lambda - A)(-1) C(X). The main result is a characterization of the generator of a C-cosine function, which may not be exponentially bounded and may have a nondensely defined generator, in terms of the associated ACP. (C) 1997 Academic Press.
