Some Research On The Properties Of Almost Periodic Type Functions

In this thesis, we investigate some properties of several classes of almost periodictype functions and their relationship. This thesis is divided into three chapters.In Chapter1, we introduce the research backgrounds and recall some definitionsand basic properties of almost periodic type functions.In Chapter2, we study the relationship between several classes of functionspaces. More specifically, we prove that the space of continuous periodic functionsis a set of first category in the space of almost periodic functions, and the space ofasymptotically almost periodic functions is always a proper subspace of the space ofweighted pseudo almost periodic functions.In Chapter3, we present an equivalent definition for weighted pseudo almostperiodic functions. Moreover, we discuss some properties of the space of weightedpseudo almost periodic functions including equivalence, translation invariance andcompleteness.