Volume 36 • Number 4 • 2013   • Convolution and Involution on Function Spaces of Homogeneous Spaces Arash Ghaani Farashahi Abstract. Let $G$ be a locally compact group and also let $H$ be a compact subgroup of $G$. It is shown that, if $\mu$ is a relatively invariant measure on $G/H$ then there is a well-defined convolution on $L^1(G/H,\mu)$ such that the Banach space $L^1(G/H,\mu)$ becomes a Banach algebra. We also find a generalized definition of this convolution for other $L^p$-spaces. Finally, we show that various types of involutions can be considered on $G/H$. 2010 Mathematics Subject Classification:43A15, 43A85 Full text: PDF