Convolutions applied on central Fourier algebras on compact groups

‎Let $G$ be a compact group and $A(G)$ be its Fourier algebra‎. ‎The speaker‎, ‎along with N‎. ‎Spronk‎, ‎investigated the range of the convolution map‎ ‎$u\otimes v\rightarrow u\ast v$ and a twisted convolution map $u\otimes v\rightarrow u\ast\check{v}$ ($\check{v}(g)=v(g^{-1})$) when applied to‎ ‎$A(G)\otimes^{h}A(G).$ We study the image of the convolution and twisted convolution map on the Haagerup tensor product of central Fourier algebras‎. ‎In the sequel‎, ‎we define a sequence of subalgebras of $A(G).$‎