Geodesic
Uniqueness for trigonometric series with respect to an increasing number of variables
Trudy Instituta matematiki i mehaniki, Function theory, Tome 11 (2005) no. 2, pp. 175-181 
N. N. Kholshchevnikova. Uniqueness for trigonometric series with respect to an increasing number of variables. Trudy Instituta matematiki i mehaniki, Function theory, Tome 11 (2005) no. 2, pp. 175-181. http://geodesic.mathdoc.fr/item/TIMM_2005_11_2_a12/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

For series with respect to Jessen’s system, an analog of the Cantor theorem on the uniqueness of a trigonometric series is proved.

[1] Jessen B., “The theory of integration in a space of infinite number of dimensions”, Acta Math., 63 (1934), 249–323 | DOI | MR

[2] Bari N. K., Trigonometricheskie ryady, Fizmatgiz, M., 1961 | MR

[3] Zigmund A., Trigonometricheskie ryady, T. 2, Mir, M., 1965 | MR

[4] Ash J. M., Welland G. V., “Convergence, uniqueness, and summability of multiple trigonometric series”, Trans. Amer. Math. Soc., 163 (1972), 401–436 | DOI | MR | Zbl

[5] Tetunashvili Sh. T., “O nekotorykh kratnykh funktsionalnykh ryadakh i reshenie problemy edinstvennosti kratnykh trigonometricheskikh ryadov dlya skhodimosti po Pringskheimu”, Mat. sb., 182:8 (1991), 1158–1176

[6] Ash J. M., Wang G., “A survey of uniqueness questions in multiple trigonometric series”, Contemporary Math., 208 (1997), 35–71 | MR | Zbl

[7] Ash J. M., Freiling C., Rinee D., “Uniqueness of rectangularly convergent trigonometric series”, Ann. of Math., 137 (1993), 145–166 | DOI | MR | Zbl