# The Heyde theorem on a-adic solenoids

Colloquium Mathematicae (2013)

- Volume: 132, Issue: 2, page 195-210
- ISSN: 0010-1354

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topMargaryta Myronyuk. "The Heyde theorem on a-adic solenoids." Colloquium Mathematicae 132.2 (2013): 195-210. <http://eudml.org/doc/284269>.

@article{MargarytaMyronyuk2013,

abstract = {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 $β₁α^\{-1\}₁ ± β₂α^\{-1\}₂$ 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.},

author = {Margaryta Myronyuk},

journal = {Colloquium Mathematicae},

keywords = {Gaussian distribution; idempotent distribution; Heyde theorem; -adic solenoid},

language = {eng},

number = {2},

pages = {195-210},

title = {The Heyde theorem on a-adic solenoids},

url = {http://eudml.org/doc/284269},

volume = {132},

year = {2013},

}

TY - JOUR

AU - Margaryta Myronyuk

TI - The Heyde theorem on a-adic solenoids

JO - Colloquium Mathematicae

PY - 2013

VL - 132

IS - 2

SP - 195

EP - 210

AB - 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 $β₁α^{-1}₁ ± β₂α^{-1}₂$ 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.

LA - eng

KW - Gaussian distribution; idempotent distribution; Heyde theorem; -adic solenoid

UR - http://eudml.org/doc/284269

ER -

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