The Heyde theorem on a-adic solenoids

• Autorzy: Margaryta Myronyuk
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 62E10: Characterization and structure theory
• 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 132
• Numer: 2
• Strony: 195-210

Daty

wydano

2013

Twórcy

autor

Margaryta Myronyuk

• B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47, Lenin Ave., Kharkov, 61103, Ukraine

Identyfikatory

DOI

10.4064/cm132-2-3