Author:
Raubenheimer H.,van Appel J.
Abstract
AbstractLet A be a Banach algebra and let $$x\in A$$
x
∈
A
have the property that its spectrum does not separate 0 from infinity. It is well known that x has a logarithm, i.e., there exists $$y\in A$$
y
∈
A
with $$x=e^y$$
x
=
e
y
. We will use this statement to identify measures defined on a locally compact group to have logarithms. Also, we will show that the converse of the above statement is in general not true. Our results will be related to infinitely divisible probability measures.
Funder
University of Johannesburg
Publisher
Springer Science and Business Media LLC
Subject
General Mathematics,Theoretical Computer Science,Analysis