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
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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.
@article{SM_1998_189_5_a0,
author = {A. S. Belov},
title = {Order estimates of the~modulus of variation of the~sum of a~lacunary trigonometric series},
journal = {Sbornik. Mathematics},
pages = {639--656},
publisher = {mathdoc},
volume = {189},
number = {5},
year = {1998},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1998_189_5_a0/}
}
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/