6 papers · 1 filter
An Analogue of Heyde's Theorem for Discrete Torsion Abelian Groups with Cyclic -Components
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 ind…
Heyde characterization theorem for some classes of locally compact Abelian groups
Gennadiy Feldman
Let and be linear forms of real-valued independent random variables. By Heyde's theorem, if the conditional distribution of given is symmetric, then the ran…
An Analogue of Heyde's Theorem for a Certain Class of Compact Totally Disconnected Abelian Groups and p-quasicyclic Groups
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 indepen…
Characterization of probability distributions on some locally compact Abelian groups containing an element of order 2
Gennadiy Feldman
The well-known Heyde theorem characterizes the Gaussian distributions on the real line by the symmetry of the conditional distribution of one linear form of independent random vari…
Heyde theorem for locally compact Abelian groups containing no subgroups topologically isomorphic to the 2-dimensional torus
Gennadiy Feldman
We prove the following group analogue of the well-known Heyde theorem on a characterization of the Gaussian distribution on the real line. Let be a second countable locally com…
On the Li--Zheng theorem
Gennadiy Feldman
By the well-known I.Kotlarski lemma, if , , and are independent real-valued random variables with nonvanishing characteristic functions, and $L_2…