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A support theorem for the complex Radon transform. (English) Zbl 0955.44001

One of the basic results on the classical Radon transform is 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 \(f\).
Reviewer: K.C.Gupta (Jaipur)

MSC:

44A12 Radon transform

Citations:

Zbl 0163.16602
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