A support theorem for the complex Radon transform (Q1566945)

One of the basic results on the classical Radon transform is \textit{S. Helgason}'s support theorem [Acta Math. 113, 153-180 (1965; Zbl 0163.16602)]: A rapidly decreasing function must vanish outside a ball if its real Radon transform does. This theorem holds for every convex compact set in \(\mathbb{R}^n\). In this paper the author investigates the relation between the supports of \(f\) and \(\widehat f\) in the case of the complex Radon transform. Here \(f\) is a function defined on \(\mathbb{R}^n\) \((\mathbb{C}^n)\) and \(\widehat f\) the classical Radon transform of \(f\).