Geodesic
On multiple Walsh series convergent over cubes
Izvestiya. Mathematics , Tome 71 (2007) no. 1, pp. 57-73.

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We consider Walsh functions on the binary group $G$ and study uniqueness sets for $N$-fold multiple Walsh series under convergence over cubes (in other words, $U_{N,\mathrm{cube}}$-sets). We prove that every finite set is a $U_{N,\mathrm{cube}}$-set, construct examples of countable $U_{N,\mathrm{cube}}$-sets and non-empty perfect $U_{N,\mathrm{cube}}$-sets, and give an example of a $U_{N,\mathrm{cube}}$-set having the maximum possible Hausdorff dimension. 
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M. G. Plotnikov. On multiple Walsh series convergent over cubes. Izvestiya. Mathematics , Tome 71 (2007) no. 1, pp. 57-73. http://geodesic.mathdoc.fr/item/IM2_2007_71_1_a4/

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