The Heyde theorem on a-adic solenoids

Margaryta Myronyuk

Colloquium Mathematicae, Tome 131 (2013), p. 195-210 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove the following analogue of the Heyde theorem for a-adic solenoids. Let ξ₁, ξ₂ be independent random variables with values in an a-adic solenoid $Σ_{a}$ and with distributions μ₁, μ₂. Let $α_{j}, β_{j}$ be topological automorphisms of $Σ_{a}$ such that $β ₁ α^{- 1} ₁ \pm β ₂ α^{- 1} ₂$ are topological automorphisms of $Σ_{a}$ too. Assuming that the conditional distribution of the linear form L₂ = β₁ξ₁ + β₂ξ₂ given L₁ = α₁ξ₁ + α₂ξ₂ is symmetric, we describe the possible distributions μ₁, μ₂.

Publié le : 2013-01-01

Zbl 1285.60005

EUDML-ID : urn:eudml:doc:284269

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     title = {The Heyde theorem on a-adic solenoids},
     journal = {Colloquium Mathematicae},
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     year = {2013},
     pages = {195-210},
     zbl = {1285.60005},
     language = {en},
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Margaryta Myronyuk. The Heyde theorem on a-adic solenoids. Colloquium Mathematicae, Tome 131 (2013) pp. 195-210. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-2-3/