On absolute convergence of Fourier series of almost periodic functions with sparse spectrum
Sbornik. Mathematics, Tome 10 (1970) no. 1, pp. 37-49
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The paper contains inequalities for the absolute value of the Fourier coefficients of functions almost periodic in the sense of Stepanov ($S$-a.p. functions) having sparse spectrum, in a sense which we define. In the particular case in which the spectrum has a single limit point at infinity, we obtain generalizations of Theorem 1 of Chao Jai-arng (RZhMat., 1967, 10B123) and Theorem 1 of Hsieh Ting-fan (RZhMat., 1967, 11B102), proved for $2\pi$-periodic functions. The case in which the spectrum has a single limit point is considered. The results are then extended to the case of $S$-a.p. functions whose spectrum has a finite or countable number of isolated limit points. It is indicated how the results may be used to give sufficient conditions for absolute convergence for the Fourier series of $S$-a.p. functions.
Bibliography: 14 titles.
@article{SM_1970_10_1_a2,
author = {E. A. Bredikhina},
title = {On absolute convergence of {Fourier} series of almost periodic functions with sparse spectrum},
journal = {Sbornik. Mathematics},
pages = {37--49},
publisher = {mathdoc},
volume = {10},
number = {1},
year = {1970},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1970_10_1_a2/}
}
E. A. Bredikhina. On absolute convergence of Fourier series of almost periodic functions with sparse spectrum. Sbornik. Mathematics, Tome 10 (1970) no. 1, pp. 37-49. http://geodesic.mathdoc.fr/item/SM_1970_10_1_a2/