  We study the Fourier transform for compactly supported distributional
sections of complex homogeneous vector bundles on symmetric spaces of
non-compact type $X = G/K$. We prove a characterisation of their range. In
fact, from Delorme's Paley-Wiener theorem for compactly supported smooth
functions on a real reductive group of Harish-Chandra class, we deduce
topological Paley-Wiener and Paley-Wiener-Schwartz theorems for sections.

Representation Theory;Analysis of PDEs;Functional Analysis