  The Radon transform and its dual are central objects in geometric analysis on
Riemannian symmetric spaces of the noncompact type. In this article we study
algebraic versions of those transforms on inductive limits of symmetric spaces.
In particular, we show that normalized versions exists on some spaces of
regular functions on the limit. We give a formula for the normalized transform
using integral kernels and relate them to limits of double fibration transforms
on spheres.
