On Sufficient Conditions for Absolute Convergence Fourier Series of Bezikovichs Almost-Periodic Functions

In this article, considered for the first time, sufficient conditions for the absolute convergence of trigonometric Fourier series of almost periodic functions in the sense of Bezikovich are obtained in the case when the Fourier exponents have a single limiting point at infinity. A higher-order continuity modulus is used as a structural characteristic of the function under consideration. Unlike periodic functions, here, in addition to the smoothness of functions, the behavior of Fourier exponents is studied when they have a single limit point at infinity, which generalizes the results of J. Museilak and N.P. Kuptsov. The paper also considers the convergence of Fourier series of almost periodic Bezikovich functions with limited variations. Similar problems for periodic functions are studied in the works of O. Sasa and S.N. Bernstein. In the final part of the article, cases are considered when Fourier exponents form a lacunar series and stronger criteria are obtained than the results of Sidon and Zigmund.