Geodesic
Uniqueness Theorems for Multiple Franklin Series Converging over Rectangles
Matematičeskie zametki, Tome 109 (2021) no. 2, pp. 206-218

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It is proved that if a multiple series in the Franklin system converges in the sense of Pringsheim everywhere, except, perhaps, on a set that is a Cartesian product of sets of measure zero, to an everywhere finite integrable function, then it is the Fourier–Franklin series of this function. A uniqueness theorem is also proved for multiple Franklin series whose rectangular partial sums at each point have a sequential limit.
Keywords: Franklin system, multiple series, uniqueness theorem. 
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     author = {G. G. Gevorkyan and L. A. Akopyan},
     title = {Uniqueness {Theorems} for {Multiple} {Franklin} {Series} {Converging} over {Rectangles}},
     journal = {Matemati\v{c}eskie zametki},
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G. G. Gevorkyan; L. A. Akopyan. Uniqueness Theorems for Multiple Franklin Series Converging over Rectangles. Matematičeskie zametki, Tome 109 (2021) no. 2, pp. 206-218. http://geodesic.mathdoc.fr/item/MZM_2021_109_2_a4/