Japanese Journal of Mathematics

, Volume 1, Issue 1, pp 87–105 | Cite as

Harmonic analysis on symmetric Stein manifolds from the point of view of complex analysis

  • Simon Gindikin


The classical theory of finite dimensional representations of compact and complex semisimple Lie groups is discussed from the perspective of multidimensional complex geometry and analysis. The key tool is the complex horospherical transform which establishes a duality between spaces of holomorphic functions on symmetric Stein manifolds and dual horospherical manifolds.

Keywords and phrases.

Stein symmetric manifolds horosphere horospherical Caushy transform 

Mathematics Subject Classification (2000).

22E30 32A26 44A12 


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Copyright information

© The Mathematical Society of Japan and Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Mathematics, Hill CenterRutgers UniversityPiscatawayUSA

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