Mean Periodic Functions on G/K
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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.
KeywordsPeriodic Function Symmetric Space Uniqueness Problem Structure Theorem Nonzero Function
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