Radon transformation on reductive symmetric spaces: Support theorems

For these transforms we derive support theorems in which the support of ϕ is (partially) characterized in terms of the support of RPϕ. The proof is based on the relation between the Radon transform and the Fourier transform on G/H, and a Paley-Wiener-shift type argument. Our results generalize the support theorem of Helgason for the Radon transform on a Riemannian symmetric space.