论文标题
Heyde定理对有限的Abelian组和形式的RXG组的概括，其中G是有限的Abelian组
Generalization of the Heyde theorem to finite Abelian groups and groups of the form RxG, where G is a finite Abelian group
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的特征在于一个单独的随机变量的一种线性形式的条件分布的对称性。我们研究该定理的某些局部紧凑的阿贝尔群体的类似物。我们考虑了两个独立随机变量的线性形式，其中具有局部紧凑的Abelian组X中的值。我们假设这些独立的随机变量的特征函数不会消失。与大多数以前的作品不同，我们对线性形式的系数没有任何限制。它们是X的任意拓扑自动形态。
According to the well-known Heyde theorem the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form of independent random variables given another. We study analogues of this theorem for some locally compact Abelian groups. We consider linear forms of two independent random variables with values in a locally compact Abelian group X. We assume that the characteristic functions of these independent random variables do not vanish. Unlike most previous works, we do not impose any restrictions on coefficients of the linear forms. They are arbitrary topological automorphisms of X.
