Convolutions on compact groups and Fourier algebras of coset spaces

Abstract

We study two related questions. (1) For a compact group $G$, what are the ranges of the convolution maps on $\mathrm{A}(G\times G)$ given for $u,v$ in $\mathrm{A}(G)$ by $u\times v\mapsto u\ast\check{v}$ ($\check{v}(s)=v(s^{-1})$) and $u\times v\mapsto u