The Annals of Probability

Zeros of the Densities of Infinitely Divisible Measures

Patrick L. Brockett and William N. Hudson

Full-text: Open access

Abstract

We consider an infinitely divisible measure $\mu$ on a locally compact Abelian group. If $\mu \ll \lambda$ (Haar measure), and if the semigroup generated by the support of the corresponding Levy measure $\nu$ is the closure of an angular semigroup, then $\mu \sim \lambda$ over the support of $\mu$. In particular, if $\int|\chi(x) - 1|\nu(dx) < \infty$, for all characters $\chi$, or if $\nu \ll \lambda$ then $\mu \ll \lambda$ implies $\mu \sim \lambda$ over the support of $\mu$.

Article information

Source
Ann. Probab., Volume 8, Number 2 (1980), 400-403.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994789

Digital Object Identifier
doi:10.1214/aop/1176994789

Mathematical Reviews number (MathSciNet)
MR566606

Zentralblatt MATH identifier
0428.60013

JSTOR
links.jstor.org

Subjects
Primary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization
Secondary: 60E05: Distributions: general theory 43A25: Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups

Keywords
Infinitely divisible measures locally Compact Abelian group absolute continuity support of measures equivalence with Haar measure

Citation

Brockett, Patrick L.; Hudson, William N. Zeros of the Densities of Infinitely Divisible Measures. Ann. Probab. 8 (1980), no. 2, 400--403. doi:10.1214/aop/1176994789. https://projecteuclid.org/euclid.aop/1176994789


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