Geodesic
On uniqueness of multiple trigonometric series
Sbornik. Mathematics, Tome 80 (1995) no. 2, pp. 335-365 
G. G. Gevorkyan. On uniqueness of multiple trigonometric series. Sbornik. Mathematics, Tome 80 (1995) no. 2, pp. 335-365. http://geodesic.mathdoc.fr/item/SM_1995_80_2_a4/
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     author = {G. G. Gevorkyan},
     title = {On uniqueness of multiple trigonometric series},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_80_2_a4/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Trigonometric series summable by the Riemann method almost everywhere are considered. In particular, it is proved that if a multiple trigonometric series sums almost everywhere by the Riemann method to an integrable function $f(x)$, and the Riemann majorant of this series satisfies a certain necessary condition, then the series is the Fourier series of the function $f(x)$.

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