Boundary Values of Eigenfunctions on Riemannian Symmetric Spaces

Abstract

We give a new and self-contained proof of a generic version of the (former) Helgason conjecture. It says that for generic spectral parameters the Poisson transform is a topological isomorphism, with the inverse given by a boundary value map. Following Oshima's approach to a simplified definition of boundary values, and using the earlier work of Baouendi and Goulaouic on Fuchsian type equations, our proof is along the lines of our earlier work in the rank one distributional case, and works for both the hyperfunction and the distribution setting.