Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group pp 487-522 | Cite as

# Mean Periodic Functions on *G*/*K*

## Abstract

The purpose of this chapter is to present extensions of the results established for Euclidean space in the previous chapter to noncompact symmetric spaces *X*=*G*/*K*. These include uniqueness theorems for mean periodic functions and related questions, structure theorems and their applications, and the finding of sharp growth conditions for mean periodic functions. If rank *X*=1, most of the Euclidean results have exact analogues for *X*. The passage to higher rank of *X* involves new features. It turned out that the main uniqueness results fail in general if rank *X**≥*2. The question when the “correct” generalization of the uniqueness result does hold is investigated. The study of the structure of mean periodic functions on *X* and finding sharp growth conditions for them depends heavily on many properties of generalized spherical functions. The corresponding results for *X* are different from that for Euclidean spaces.

## Keywords

Periodic Function Symmetric Space Uniqueness Problem Structure Theorem Nonzero Function## Preview

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