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ℰ′(X) Spectral Analysis on Domains of Noncompact Symmetric Spaces of Arbitrary Rank

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

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 rankX=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 
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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