On logarithms of measures

IF 0.8 3区数学 Q2 MATHEMATICS

Positivity Pub Date : 2023-10-16 DOI:10.1007/s11117-023-01015-2

H. Raubenheimer, J. van Appel

引用次数: 0

Abstract

Abstract Let 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.

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关于测度的对数

摘要设A是一个Banach代数，且设$$x\in A$$ x∈A具有其谱不将0与无穷分开的性质。众所周知，x有对数，即存在$$y\in A$$ y∈a，且$$x=e^y$$ x = ey。我们将使用这个语句来确定在局部紧群上定义的具有对数的测度。同样，我们将证明上述陈述的反面通常是不正确的。我们的结果将与无限可分的概率测度有关。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Positivity 数学-数学

CiteScore

1.80

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： The purpose of Positivity is to provide an outlet for high quality original research in all areas of analysis and its applications to other disciplines having a clear and substantive link to the general theme of positivity. Specifically, articles that illustrate applications of positivity to other disciplines - including but not limited to - economics, engineering, life sciences, physics and statistical decision theory are welcome. The scope of Positivity is to publish original papers in all areas of mathematics and its applications that are influenced by positivity concepts.