Helgason Fourier transform

Summary

The Helgason Fourier transform is the Fourier transform on a Riemannian symmetric space $X = G / K$ of noncompact type. It expands a function on $X$, not only a radial one, in plane waves $e^{(i \lambda + \rho)(A(x, b))}$ indexed by a frequency $\lambda$ and a boundary point $b$. On radial functions it reduces to the spherical transform. It satisfies an inversion formula and a Plancherel formula with the density $\abs{c(\lambda)}^{-2}$ of the Harish-Chandra c-function.