Zeros of the densities of infinitely divisible measures on \(\mathbb{R}^ n\) (Q678095)

It is a hard problem to get information about the densities of infinitely divisible multivariate measures \(\mu\) which are given by their Lévy-Khinchin formula of their characteristic functions. It was an open problem whether absolutely continuous \(\mu\) are equivalent with Lebesgue measure on their support. The authors attack the problem again by a new decomposition of the set of admissible translates. They obtain a unified approach for earlier results and an affirmative answer for \(\mu\)'s with full support \(\mathbb{R}^n\). This result follows if their arguments are combined with \textit{J. Yuan}'s theorems [Semigroup Forum 27, 377-386 (1983; Zbl 0539.60020)].