On the Uniqueness Sets of Multiple Walsh Series for Convergence in Cubes

Let $G^d$ be a power of the Cantor binary group $G$. The uniqueness problem for a multiple Walsh series on a power of the binary group in the case of convergence in cubes is discussed. It is proved that if $x\in G^{d-1}$, then $G\times \{x\}$ is the uniqueness set of a $d$-dimensional Walsh series in the case of convergence in cubes.