Geodesic
Order estimates of the modulus of variation of the sum of a lacunary trigonometric series
Sbornik. Mathematics, Tome 189 (1998) no. 5, pp. 639-656 Cet article a éte moissonné depuis la source Math-Net.Ru

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We find order estimates for the modulus of variation and the averaged modulus of the sum of a lacunary trigonometric series in terms of its coefficients. These interesting global characteristics of a function and their applications have been studied in papers by Chanturiya, Dolzhenko, Sevast'yanov, Sendov, Popov, and others. Since the sum of a lacunary trigonometric series has frequently been used in the theory of functions to provide an example of a function having one property or another, it is useful to know as much as possible about such a function, especially such global characteristics as the modulus of variation and the averaged modulus. We also give necessary and sufficient conditions for the sum of a lacunary trigonometric series to belong to certain classes of functions defined in terms of these characteristics. 
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     title = {Order estimates of the~modulus of variation of the~sum of a~lacunary trigonometric series},
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A. S. Belov. Order estimates of the modulus of variation of the sum of a lacunary trigonometric series. Sbornik. Mathematics, Tome 189 (1998) no. 5, pp. 639-656. http://geodesic.mathdoc.fr/item/SM_1998_189_5_a0/

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