Geodesic
Union of sets of uniqueness for multiple Walsh and multiple trigonometric series
Sbornik. Mathematics, Tome 193 (2002) no. 4, pp. 609-633 Cet article a éte moissonné depuis la source Math-Net.Ru

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For the case of convergence over rectangles of multiple Walsh and multiple trigonometric series questions on unions of sets of uniqueness, formal multiplication of series, the localization principle for integrable functions, and analogues of Privalov's theorem on the unique representation of a function by a series are considered. 
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N. N. Kholshchevnikova. Union of sets of uniqueness for multiple Walsh and multiple trigonometric series. Sbornik. Mathematics, Tome 193 (2002) no. 4, pp. 609-633. http://geodesic.mathdoc.fr/item/SM_2002_193_4_a6/

[1] Skvortsov V. A., “O koeffitsientakh skhodyaschikhsya kratnykh ryadov Khaara i Uolsha”, Vestn. MGU. Ser. 1. Matem., mekh., 1973, no. 6, 77–79 | Zbl

[2] Movsisyan Kh. O., “O edinstvennosti dvoinykh ryadov po sistemam Khaara i Uolsha”, Izv. AN Arm. SSR. Matem., 9:1 (1974), 40–61 | MR

[3] Lukomskii S. F., “O nekotorykh klassakh mnozhestv edinstvennosti kratnykh ryadov Uolsha”, Matem. sb., 180:7 (1989), 937–945 | MR

[4] Ash J. M., Welland G. V., “Convergence, uniqueness and summability of multiple trigonometric series”, Trans. Amer. Math. Soc., 163:1 (1972), 401–436 | DOI | MR | Zbl

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

[6] Golubov B. I., Efimov A. V., Skvortsov V. A., Ryady i preobrazovaniya Uolsha, Nauka, M., 1987 | MR | Zbl

[7] Privalov I. I., “Obobschenie teoremy P. Du Bois-Reymond'a”, Matem. sb., 31:2 (1923), 229–231

[8] Skvortsov V. A., “Nekotorye obobscheniya teoremy edinstvennosti dlya ryadov po sisteme Uolsha”, Matem. zametki, 13:3 (1973), 367–372 | MR | Zbl

[9] Kholschevnikova N. N., “Teoremy ob ob'edinenii $U$-mnozhestv”, Matem. zametki, 67:5 (2000), 778–787 | MR

[10] Skvortsov V. A., Talalyan A. A., “Nekotorye voprosy edinstvennosti kratnykh ryadov po sisteme Khaara i trigonometricheskoi sisteme”, Matem. zametki, 46:2 (1989), 104–113 | MR

[11] Kuratovskii K., Topologiya, T. 1, Mir, M., 1966 | MR

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

[13] Kahane S., “Antistable classes of thin sets in harmonic analysis”, Illinois J. Math., 37 (1993), 186–223 | MR | Zbl

[14] Konyagin S. V., “Every set of resolution is an Arbault set”, C. R. Acad. Sci. Paris. Sér. I Math., 314 (1992), 101–104 | MR | Zbl

[15] Kholschevnikova N. N., “O teoreme Kantora–Lebega dlya kratnykh trigonometricheskikh ryadov”, Fundament. fiziko-matem. problemy, Sb. nauchnykh trudov, no. 3, 2000, 35–40