Geodesic
A~uniqueness theorem for multiple Lacunary trigonometric series
Matematičeskie zametki, Tome 16 (1974) no. 6, pp. 865-870

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Uniqueness theorems for multiple trigonometric series which are lacunary with respect to all or some of the variables are obtained. 
@article{MZM_1974_16_6_a1,
     author = {V. F. Gaposhkin},
     title = {A~uniqueness theorem for multiple {Lacunary} trigonometric series},
     journal = {Matemati\v{c}eskie zametki},
     pages = {865--870},
     publisher = {mathdoc},
     volume = {16},
     number = {6},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_6_a1/}
}
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V. F. Gaposhkin. A~uniqueness theorem for multiple Lacunary trigonometric series. Matematičeskie zametki, Tome 16 (1974) no. 6, pp. 865-870. http://geodesic.mathdoc.fr/item/MZM_1974_16_6_a1/