论文标题
在Heyde定理的本地紧凑型Abelian群体上，其中包含命令2的元素
On Heyde's theorem for locally compact Abelian groups containing elements of order 2
论文作者
论文摘要
根据众所周知的Heyde定理，实际线上的高斯分布类别的特征是一种线性分布的一种线性分布的对称性，即给定的独立随机变量的一种线性形式。我们研究了该定理的类似物对某些局部紧凑的Abelian组X，其中包含命令2的元素。我们证明，如果X包含订单2的元素，则可以导致以下事实：X上的一类广泛的非高斯分布的特征是一种固定形式的条件分布的对称性。在这样做线性形式的系数中，是X的拓扑自动形态。
According to the well-known Heyde theorem the class of Gaussian distributions on the real line is characterized by the symmetry of the conditional distribution of one linear form of independent random variables given the other. We study analogues of this theorem for some locally compact Abelian groups X containing an element of order 2. We prove that if X contains an element of order 2, this can lead to the fact that a wide class of non-Gaussian distributions on X is characterized by the symmetry of the conditional distribution of one linear form given the other. In so doing coefficients of linear forms are topological automorphisms of X.
