Geodesic
On~some uniqueness properties of multiple trigonometric series and harmonic functions
Izvestiya. Mathematics , Tome 32 (1989) no. 3, pp. 627-654

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Some uniqueness theorems for multiple trigonometric series $\sum_na_ne^{2\pi inx}$ are established, where the an are bounded and tend to zero, when all the coordinates of the vector $n$ tend to infinity. Some boundary uniqueness properties for $m$-harmonic functions are also established. Bibliography: 8 titles. 
@article{IM2_1989_32_3_a8,
     author = {A. A. Talalyan},
     title = {On~some uniqueness properties of multiple trigonometric series and harmonic functions},
     journal = {Izvestiya. Mathematics },
     pages = {627--654},
     publisher = {mathdoc},
     volume = {32},
     number = {3},
     year = {1989},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1989_32_3_a8/}
}
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A. A. Talalyan. On~some uniqueness properties of multiple trigonometric series and harmonic functions. Izvestiya. Mathematics , Tome 32 (1989) no. 3, pp. 627-654. http://geodesic.mathdoc.fr/item/IM2_1989_32_3_a8/