Browsing by Author "Samal, Jajati Keshari"

Now showing 1 - 1 of 1
  • Thumbnail Image
    Item
    Almost Periodic Functions and Their Applications
    (Department of Mathematics, NITS, 2025) Samal, Jajati Keshari
    Periodic functions are among the most frequently occurring classes of functions in both applied and analytical mathematics. Due to this wide range of applicability, we aim to extend this class of functions to enable broader analysis. The extended class we discuss is known as almost periodic functions. In this thesis, we begin by exploring the motivation for and development of almost periodic functions, which arise from the theory of periodic functions in Chapter 1. Chapter 2 presents the history of the development of almost periodic functions. In Chapter 3, we revisit some fundamental results from analysis that are useful for our proofs. Chapter 4 reviews key properties and characterizations of almost periodic functions, including Bochner’s criterion, and provides relevant counterexamples. In Chapter 5, we discuss important applications of these functions in the context of ordinary differential equations. Finally, Chapter 6 concludes the thesis with the future scope of almost periodic functions.