Almost periodic functions on time scales and their properties

Source abstract

Abstract In this article, we first propose a concept of almost periodic functions on arbitrary time scales, which is defined by trigonometric polynomial approximations with respect to supremum norm, and study some basic properties of these kinds of functions. Then, on almost periodic time scales, we introduce the concepts of the mean value and Fourier series of almost periodic functions and give some related results. Finally, we give the definitions of almost periodic functions in the sense of Bohr and in the sense of Bochner on time scales, respectively, and prove the equivalence of the above three definitions on almost periodic time scales.