Zeros of the densities of infinitely divisible measures on \(\mathbb{R}^ n\)
type: Item
instance of: scholarly article
title: Zeros of the densities of infinitely divisible measures on \(\mathbb{R}^ n\)
zbMATH Open document ID: 0883.60013
DOI: 10.1007/BF02214662
author: Tomasz Byczkowski
author: Balram S. Rajput
author: Tomasz Żak
published in: Journal of Theoretical Probability
publication date: 1998-03-16T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 60E07
zbMATH DE Number: 1000181
zbMATH Keywords: infinitely divisible measures
zbMATH Keywords: equivalence with Lebesgue measure
zbMATH Keywords: admissible translates
zbMATH Keywords: angular semigroup
reviewed by: Arnold Janssen
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02214662
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description: scientific article; zbMATH DE number 1000181