Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group pp 615-631 | Cite as

# ℰ′_{♮♮}(*X*) Spectral Analysis on Domains of Noncompact Symmetric Spaces of Arbitrary Rank

## Abstract

In this chapter a new approach to problems of spectral analysis on symmetric spaces *X*=*G*/*K* is developed. The main advantage of this approach is that it enables us to prove a symmetric space analog of the local version of the Brown–Schreiber–Taylor theorem and investigate the problem of existence of a nontrivial solution for systems of convolution equations in more detail. For the case where rank*X*=1, some new results concerning the exponential representation problem are also presented. The remainder of the chapter consists of applications to the Zalcman two-radii problem on *X*, which deals with the characterization of a function via integral ball means. When the group *G* is complex, a definitive local version of the Zalcman two-radii theorem is proved.

## Keywords

Spectral Analysis Periodic Function Symmetric Space Local Version Nontrivial Solution## Preview

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