3 papers
math.PR2023
Heyde theorem on locally compact Abelian groups with the connected component of zero of dimension 1
Gennadiy Feldman
Let be a locally compact Abelian group with the connected component of zero of dimension 1. Let and be independent random variables with values in with nonvanis…
math.PR2023
On a characterization of shifts of Haar distributions on compact open subgroups of a compact Abelian group
Gennadiy Feldman
Let X be a compact Abelian group. In the article we obtain a characterization of shifts of Haar distributions on compact open subgroups of the group X by the symmetry of the condit…
math.PR2022
Generalization of the Heyde theorem to finite Abelian groups and groups of the form RxG, where G is a finite Abelian group
Gennadiy Feldman
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 independ…