论文标题
$ \ mathbb {r}^n \ times d $上的heyde定理，其中$ d $是一个离散的abelian group
The Heyde theorem on a group $\mathbb{R}^n\times D$, where $D$ is a discrete Abelian group
论文作者
论文摘要
海德证明了实际线上的高斯分布的特征是一个线性统计量给定的条件分布的对称性。本文致力于Heyde定理的小组类似物。我们描述了独立随机变量$ξ_1$，$ξ_2$的分布，其中一个值$ x = \ m马理{r}^n \ times d $，其中$ d $是一个离散的阿贝尔集团，其特征在于线性统计$ l_2 = $ l_2 = end_1 +δ_2$δ_2$ l_2 $ l_2 $ l_2 $ l_2 $ l_2 $ l_2 $ l_2 $δ$是$ x $的拓扑自动形态，因此$ {ker}（i+δ）= \ {0 \} $。
Heyde proved that a Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear statistic given another. The present article is devoted to a group analogue of the Heyde theorem. We describe distributions of independent random variables $ξ_1$, $ξ_2$ with values in a group $X=\mathbb{R}^n\times D$, where $D$ is a discrete Abelian group, which are characterized by the symmetry of the conditional distribution of the linear statistic $L_2 = ξ_1 + δξ_2$ given $L_1 = ξ_1 + ξ_2$, where $δ$ is a topological automorphism of $X$ such that ${Ker}(I+δ)=\{0\}$.
