| Popis: |
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, Proc. Japan Acad. 42 (1966), 308-312 and Theorem 1 of Hsieh Ting-fan, Acta Math. Sinica 16 (1966), 513-516, proved for 2π-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 items. |
