Mean Periodic Functions on Compact Symmetric Spaces of Rank One

Abstract

The chapter develops the theory of mean periodic functions on compact symmetric spaces. Various support properties of mean periodic functions on compact symmetric spaces $\mathcal{X}$ of rank one are discussed. Presented are diverse characterizations of mean periodic functions on subsets of $\mathcal{X}$ . The case of the whole space $\mathcal{X}$ is considered later in more general context. In contrast to the noncompact case, these questions involve additional difficulties related to finding explicit formulas for differential operators from the Lie algebra of the isometry group. The corresponding formulas are presented in the first section of the chapter.