Symmetric Spaces of Rank 1

  • Sundaram Thangavelu
Part of the Progress in Mathematics book series (PM, volume 217)


In this chapter our aim is to formulate and prove an analogue of Hardy’s theorem for the Helgason Fourier transform on the complex hyperbolic space. Though most of the results proved in this chapter including Hardy’s theorem are true for any rank 1 symmetric space we restrict ourselves to the hyperbolic space. We develop spherical and Helgason Fourier transforms, Hecke-Bochner formulas, Jacobi transforms and heat kernel estimates that are needed for proving Hardy’s theorem.


Symmetric Space Heat Kernel Radial Function Spherical Function Inversion Formula 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Sundaram Thangavelu
    • 1
  1. 1.Statistics and Mathematics DivisionIndian Statistical InstituteBangaloreIndia

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