The Heyde characterization theorem on some locally compact Abelian groups

Abstract

By the Heyde theorem, the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form of of $n$ independent random variables given another. When $n=2$ we prove analogues of this theorem in the case when independent random variables take values in a locally compact Abelian group $X$ and coefficients of the linear forms are topological automorphisms of $X$.

Cited by in corpus (5)

• Characterization of distributions of $Q$-independent random variables on locally compact Abelian groups
• On notions of Q-independence and Q-identical distributiveness
• On a characterisation theorem for $a$-adic solenoids
• The Heyde characterization theorem on compact totally disconnected and connected Abelian groups
• On a characterisation theorem for probability distributions on discrete Abelian groups