Geodesic
On some multiple functionseries and solution of the uniqueness problem for Pringsheim convergence of multiple trigonometric series
Sbornik. Mathematics, Tome 73 (1992) no. 2, pp. 517-534

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Uniqueness theorems are proved for some multiple function series. A particular consequence of these theorems is the solution of a uniqueness problem for multiple trigonometric series. One result is the following proposition: any countable set is a set of uniqueness (for Pringsheim convergence) of $d$-fold trigonometric series $(d\geqslant 2)$. 
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     author = {Sh. T. Tetunashvili},
     title = {On some multiple functionseries and solution of the uniqueness problem for {Pringsheim} convergence of multiple trigonometric series},
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     url = {http://geodesic.mathdoc.fr/item/SM_1992_73_2_a13/}
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Sh. T. Tetunashvili. On some multiple functionseries and solution of the uniqueness problem for Pringsheim convergence of multiple trigonometric series. Sbornik. Mathematics, Tome 73 (1992) no. 2, pp. 517-534. http://geodesic.mathdoc.fr/item/SM_1992_73_2_a13/