On absolute convergence of Fourier series of almost periodic functions with sparse spectrum

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.