The support theorem for the complex Radon transform of distributions

الأصل · EN

The complex Radon transform F of a rapidly decreasing distribution F∈OC′(Cⁿ) is considered. A compact set Kⁿ is called linearly convex if the set Cⁿ K is a union of complex hyperplanes. Let K denote the set of complex hyperplanes which meet K. The main result of the paper establishes the conditions on a linearly convex compact K under which the support theorem for the complex Radon transform is true: from the relation supp(F)⊂ K it follows that F∈O′C(Cⁿ) is compactly supported and supp(F)⊂ K.