Periodic and Almost Periodic Functions. Brief Introduction

In this chapter, we describe in brief the main classes of functions that we shall use in what follows. The functions of these classes are determined for all t ∈ (−∞,∞) (we shall write t ∈ R).

We shall associate each periodic function f(t) with the period T (it is not necessary that the function be continuous) a Fourier series

f(t) ∼ a0 + ∞∑

ak cos 2π T

kt + bk sin 2π T

kt.