Geodesic
Uniqueness theorems for multiple Franklin series
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 3, pp. 241-249

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It is proved, that if the square partial sums $\sigma_{q_n}(x)$ of a multiple Franklin series converge in measure to a function $f$, the ratio $\dfrac{q_{n+1}}{q_n}$ is bounded and the majorant of partial sums satisfies to a necessary condition, then the coefficients of the series are restored by the function $f$.
Keywords: majorant of partial sums, $A$-integral, uniqueness. 
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K. A. Navasardyan. Uniqueness theorems for multiple Franklin series. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 3, pp. 241-249. http://geodesic.mathdoc.fr/item/UZERU_2017_51_3_a5/