Geodesic
Quasianalyticity of the sum of a lacunary series
Sbornik. Mathematics, Tome 28 (1976) no. 3, pp. 389-419 Cet article a éte moissonné depuis la source Math-Net.Ru

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We present a simple method, which as far as we know is different from all previous methods, for proving a theorem of Mandelbrojt (Quasianafytic classes of functions, ONTI, Leningrad–Moscow, 1937, p. 84) and its generalizations. It is shown that this method leads to very precise theorems for lacunary series. Bibliography: 5 titles. 
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A. S. Belov. Quasianalyticity of the sum of a lacunary series. Sbornik. Mathematics, Tome 28 (1976) no. 3, pp. 389-419. http://geodesic.mathdoc.fr/item/SM_1976_28_3_a8/

[1] S. Mandelbroit, Kvazianaliticheskie klassy funktsii, ONTI, Moskva, 1937

[2] S. Mandelbrojt, N. Wiener, “Séries de Fourier lacunaires. Théorèmes inverses”, C. r. Acad. scient. Paris, 203 (1936), 34–36 ; 233–234 | Zbl | Zbl

[3] B. Ya. Levin, M. Livshits, “O kvazianaliticheskikh klassakh funktsii, predstavlennykh ryadami Fure”, Matem. sb., 9 (51) (1941), 693–709

[4] B. Ya. Levin, Raspredelenie kornei tselykh funktsii, Gostekhizdat, Moskva, 1956

[5] A. Zigmund, Trigonometricheskie ryady, t. I, izd-vo «Mir», Moskva, 1965 | MR