Metric Space-Valued Almost Periodic Functions And Almost Automorphic Functions On Groups

In the previous studies about almost periodic functions and almost automorphic functions on groups,most of them are based on complex space.Therefore,in this paper,we will explore some properties of Banach-valued almost periodic functions on groups and almost automorphic functions on groups which range is in metric space The main contents includeChapter 1,we introduce the development of almost periodic function theory,including almost automorphic functions and almost periodic functions on groupsChapter 2,we introduce the basic knowledge and related results of classical almost periodic functions and complex valued almost periodic functions on groups,Then we give the basic concepts of the metric space-valued almost periodic functions on groups and properties,and we prove that the left almost periodic functions and the right almost periodic functions on groups with values in Banach spaces which are finite-dimensional are equivalent.In addition,we study the conditions of normal sequences and the properties of translation sets of almost periodic functions on locally compact Abelian groups,and obtain some relevant resultsChapter 3,we introduce the preparatory knowledge and related contents of almost automorphic functions on groups which range is in metric space and get rel-vant results.In this chapter,we extend the range of almost automorphic functions on groups from complex space to metric space and Bohr almost automorphic functions and study their general properties and obtain a series of results.