S. Johansen has given a
characterization of infinitely divisible characteristic functions on the real line
analogous to the Bochner’s theorem characterizing the characteristic functions
through their nonnegative definiteness. Recently the present author was able to
extend this result to infinitely divisible characteristic functionals on a Hilbert space
and on locally compact abelian groups. We shall now obtain a similar theorem for
infinitely divisible characteristic functionals on locally convex topological vector
spaces whose dual spaces are nuclear.