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Mean Periodic Functions on G/K

  • Valery V. VolchkovEmail author
  • Vitaly V. Volchkov
Part of the Springer Monographs in Mathematics book series (SMM)

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 X2. 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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London Limited 2009

Authors and Affiliations

  1. 1.Mathematical DepartmentDonetsk National UniversityDonetskUkraine

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