Operator exponents of probability measures and Lie semigroups
type: Item
instance of: scholarly article
title: Operator exponents of probability measures and Lie semigroups
zbMATH Open document ID: 0779.60007
author: Zbigniew J. Jurek
published in: The Annals of Probability
publication date: 1993-01-16T00:00:00Z
review text: \(U\)-exponents of probability measure on a linear space are introduced. These are bounded linear operators, and it is shown that the set of all \(U\)-exponents form a Lie wedge for full measures on finite-dimensional spaces. This allows the construction of \(U\)-exponents commuting with the symmetry group of a measure. The set of all commuting exponents is described and elliptically symmetric measures are characterized in terms of their Fourier transforms. Also, self-decomposable measures are identified among those which are operator-self-decomposable. Finally, \(S\)-exponents of infinitely divisible measures are discussed.
Mathematics Subject Classification ID: 60B15
Mathematics Subject Classification ID: 22A15
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 60E07
zbMATH DE Number: 89801
zbMATH Keywords: \(U\)-exponents
zbMATH Keywords: symmetry group of a measure
zbMATH Keywords: self-decomposable measures
zbMATH Keywords: operator-self-decomposable
zbMATH Keywords: infinitely divisible measures
reviewed by: Yasuhiro Asoo
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176989817
OpenAlex ID: W2020395347
DOI: 10.1214/AOP/1176989817
description: scientific article; zbMATH DE number 89801