Symmetric Spaces of Rank 1
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.
KeywordsSymmetric Space Heat Kernel Radial Function Spherical Function Inversion Formula
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