Supports of Infinitely Divisible Measures on Hilbert Space

Abstract

The supports of infinitely divisible measures on separable Hilbert spaces are characterized in terms of angular semigroups. Restricted to $\mathbb{R}^n$ this result extends results of Hudson and Mason. Restricted to $\mathbb{R}^1$ our result improves Tucker's result and Hudson and Tucker's results on such supports. Also investigated are the supports of stable measures on Hilbert space.