The Heyde characterization theorem on some locally compact Abelian groups

2017/02/07 by Feldman, G. M.
#43A35 #60B15 #62E10 #FOS: Mathematics #Group Theory (math.GR) #Probability (math.PR)

paper · doi:10.48550/arxiv.1702.01913

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.

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