Geodesic
On Heyde's theorem on the group $\mathbb{R}\times\mathbb{T}$
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 493 (2020), pp. 42-46 Cet article a éte moissonné depuis la source Math-Net.Ru

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According to the well-knows 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 the other. We study analogues of this theorem for some locally compact Abelian groups that contain an element of order 2. While coefficients of linear forms are topological automorphisms of a group.
Keywords: Heyde theorem, locally compact Abelian group, topological automorphism. 
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G. M. Feldman. On Heyde's theorem on the group $\mathbb{R}\times\mathbb{T}$. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 493 (2020), pp. 42-46. http://geodesic.mathdoc.fr/item/DANMA_2020_493_a8/

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