局部紧阿贝尔群上的部分可分概率测度
Partly divisible probability measures on locally compact Abelian groups
摘要：
在具有连通对偶群$\hat G=\R^d\times \T^n$的局部紧阿贝尔群$G$上定义了容许概率测度$μ$.对于这样的测度$μ$，可以关联闭半群$Λ(μ)\subseteq (0,\infty)$，使得对于$t\in Λ(μ)$，对$t$的幂的傅立叶变换$(\hat μ)^t$是特征函数。本文证明了非容许概率测度根的存在性是基于一些限制条件，而这些限制条件在容许情形下是不成立的。正如我们在例子$\Z_2$中所证明的，在具有非连通对偶群的LCA-群的情况下，没有集合$Λ(μ)$的规范定义。
英文摘要：
A notion of admissible probability measures $μ$ on a locally compact Abelian group (LCA-group) $G$ with connected dual group $\hat G=\R^d\times \T^n$ is defined. To such a measure $μ$, a closed semigroup $Λ(μ)\subseteq (0,\infty)$ can be associated, such that, for $t\in Λ(μ)$, the Fourier transform to the power $t$, $(\hat μ)^t$, is a characteristic function. We prove that the existence of roots for non admissible probability measures underlies some restrictions, which do not hold in the admissible case. As we show for the example $\Z_2$, in the case of LCA-groups with non connected dual group, there is no canonical definition of the set $Λ(μ)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
