The support theorem for the complex Radon transform of distributions

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dc.creatorSekerin, A. B.
dc.date2003-11-17
dc.date.accessioned2026-07-07T05:02:58Z
dc.date.available2026-07-07T05:02:58Z
dc.descriptionThe complex Radon transform $\hat F$ of a rapidly decreasing distribution $F\in\mathscr{O}_C^{\prime}(\mathbb{C}^n)$ is considered. A compact set $K\subset\mathbb{C}^n$ is called linearly convex if the set $ \mathbb{C}^n \setminus K$ is a union of complex hyperplanes. Let $\hat K$ 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 $\hbox{supp}(\hat F)\subset\hat K$ it follows that $F\in\mathscr{O}^{\prime}_C(\mathbb{C}^n)$ is compactly supported and $\hbox{supp}(F)\subset K$.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/math/0311277
dc.identifierhttp://arxiv.org/abs/math/0311277
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69222
dc.subjectComplex Variables
dc.subjectFunctional Analysis
dc.subject44A12 (Primary) 46F10, 46F12, 30E99 (Secondary)
dc.titleThe support theorem for the complex Radon transform of distributions
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