Hypergroups with Unique Alpha-Means
Abstract
Description
Let $K$ be a commutative hypergroup and $α\in \hat{K}$. We show that $K$ is $α$-amenable with the unique $α$-mean $m_α$ if and only if $m_α\in L^1(K)\cap L^2(K)$ and $α$ is isolated in $\hat{K}$. In contrast to the case of amenable noncompact locally compact groups, examples of polynomial hypergroups with unique $α$-means ($α\not=1$) are given. Further examples emphasize that the $α$-amenability of hypergroups depends heavily on the asymptotic behavior of Haar measures and characters.
8 pages, keywords: Hypergroups: orthogonal polynomial, of Nevaei classes. $α$-Amenable Hypergroups
8 pages, keywords: Hypergroups: orthogonal polynomial, of Nevaei classes. $α$-Amenable Hypergroups