Infinitely divisible characteristic functionals on locally convex topological vector spaces

B. L. S. Prakasa Rao

Vol. 35 (1970), No. 1, 221–225

DOI: 10.2140/pjm.1970.35.221

Abstract

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.

Mathematical Subject Classification

Primary: 46.01

Secondary: 42.00

Milestones

Received: 13 November 1969

Published: 1 October 1970