  Let $G$ be a compact group and let $A^n(G)$ denote the multidimensional
Fourier algebra introduced by Todorov and Turowska. In this note, we first
define the multidimensional version of the Varopolous algebra and show that the
multidimensional Fourier algebra can be embedded into the multidimensional
Varopolous algebra. Using this embedding, we also prove a result on parallel
synthesis, subsuming the earlier results of Varopolous, Spronk-Turowska and
Parthsarathy-Prakash.
