Abstract:
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.