Regular Almost-Periodic Functions and the Concept of Periodicity

The present paper investigates the concept of regular almost-periodic functions and their fundamental properties as a natural generalization of classical periodic functions. Special attention is paid to the notion of ε-periods and their role in describing quasi-periodic behavior on the real line. The study clarifies the mathematical essence of almost periodicity in the sense of Bohr and highlights the importance of relative density of ε-periods. Key structural properties of regular almost-periodic functions are discussed, emphasizing their stability under algebraic operations and translations. The relevance of these functions in the theory of differential equations and in the modeling of physical and technical systems is also briefly addressed. The results demonstrate that regular almost-periodic functions constitute an effective analytical tool for describing complex processes that cannot be adequately modeled using classical periodic functions.