On uniqueness of multiple trigonometric series
Sbornik. Mathematics, Tome 60 (1988) no. 1, pp. 107-131 Cet article a éte moissonné depuis la source Math-Net.Ru

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This article is devoted to questions of the uniqueness of multiple trigonometric series. Uniqueness theorems are obtained for multiple trigonometric series with additional hypotheses on their coefficients or spherical Abel means, and also on their Lebesgue means. Bibliography: 19 titles
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A. A. Talalyan. On uniqueness of multiple trigonometric series. Sbornik. Mathematics, Tome 60 (1988) no. 1, pp. 107-131. http://geodesic.mathdoc.fr/item/SM_1988_60_1_a6/

[1] Cohen P. J., “Topics in the theory of uniqueness of trigonometrical series”, Thesis. University of Chicago, III, 1958

[2] Shapiro V. A., “Uniqueness of multiple trigonometric series”, Ann. Math., 66:3 (1957), 467–480 | DOI | MR | Zbl

[3] Shapiro V. A., “Sets of uniquencess on the 2-Torus”, Amer. Math. Soc., 165. March (1972), 127–147 | DOI | MR | Zbl

[4] Hedberg T., “On the uniqueness of summable trigonometric series and integrals”, Ark. Mat., 9:2 (1971), 223–241 | DOI | MR | Zbl

[5] Ash J., Welland G., “Convergence, summability and uniqueness of multiple trigonometric series”, Trans. Amer. Math. Soc., 163 (1972), 401–445 | DOI | MR

[6] Minakshisundaran S., “A uniqueness theorem for eigenfunction expansions”, Proc. Nat. Acad. Sci. USA., 33:1 (1974), 76–77 | MR

[7] Connes B., “Unicite des series trigonometriques a une ou piosieurs variables”, Thes. doct. Sci. Math. Univ., Paris-Sud, 1978

[8] Connes B., “Sur les coefficients des series trigonometriques convergentes spheriguement”, C. R. Acad. Sci. Paris, 283 (1976), 159–161 | MR | Zbl

[9] Cooke R., “Cantor–Lebesque theorem in two dimensions”, Proc. Amer. Math. Soc., 30:3 (1971), 547–550 | DOI | MR | Zbl

[10] Zygmund A. A., “Cantor–Lebesque theorem for double trigonometric series”, Studia Math., 43:2 (1972), 171–175 | MR

[11] Kuratsubo Shigehiko, “Note of Fourier Coefficients”, Sci. Repts. Hirosaki Univ., 21:1 (1979), 26–29 | MR

[12] Arutyunyan F G., Talalyan A. A., “O edinstvennosti ryadov po sistemam Khaara i Uolsha”, Izv. AN SSSR. Ser. matem., 28 (1964), 1391–1408 | Zbl

[13] Movsisyan Kh. O., “O edinstvennosti dvoinykh ryadov po sistemam Khaara i Uolsha”, Izv. AN ArmSSR. Ser. matem., 9 (1974), 40–61

[14] Skvortsov V. A., “O mnozhestvakh edinstvennosti dlya mnogomernykh ryadov Khaara”, Matem. zametki, 14:6 (1973), 789–798 | Zbl

[15] Golubov B. I., “O metode summirovaniya tipa Abelya–Puassona kratnykh ryadov Fure”, Matem. zametki, 27:1 (1980), 49–59 | MR | Zbl

[16] Zigmund A., Trigonometricheskie ryady, T. I, Mir, M., 1965. | MR

[17] Zigmund A., Trigonometricheskie ryady, T. II, Mir, M., 1965. | MR

[18] Stein I., Veis G., Vvedenie v garmonicheskii analiz na evklidovykh prostranstvakh, Mir, M., 1974 | Zbl

[19] Zhizhiashvili L. V., “O nekotorykh voprosakh iz teorii prostykh i kratnykh trigonometricheskikh i ortogonalnykh ryadov”, UMN, 28:2 (1973), 65–119 | MR