On Khinchin's formula for compact hypergroups (Q909329)

In the article the Khinchin representation for probability measures on commutative compact hypergroups is obtained. Theorem. Every probability measure \(\mu({\hat \mu}(\chi)\neq 0)\) on a commutative compact hypergroup K can be represented as \(\mu =\gamma_ 1*\gamma_ 2\) where \(\gamma_ 1\) is an at most countable convolution of indecomposable measures and \(\gamma_ 2\) has no indecomposable divisors. The Theorem can be extended onto a locally compact hypergroup \(K_ 1\) if the support of the Plancherel measure coincides with \(\hat K_ 1\) and there exists a sequence \(Q_ 1\subseteq Q_ 2\subseteq Q_ 3\subseteq...\subseteq \hat K_ 1\) (every \(Q_ j\) is compact) such that \(\hat K_ 1=\cup^{\infty}_{j=1}Q_ j\). This result was reported at the conference of young scientists, Math. Inst. Acad. Sci. UkrSSR, June 15-17, Kiev (1988).