Resumen de A support theorem for the complex Radon transform

A. B. Sekerin

• Let $C_c(\mathbb{C}^n)$ be the space of compactly supported continuous functions on $\mathbb{C}^n$. For $f\in C_c(\mathbb{C}^n),\hat f$ denotes the complex Radon transform of $f$. We say that for a compact set $K$ the support theorem holds if every function $\varphi\in C_c(\mathbb{C}^n)$ with supp$(\hat\varphi)\subset\hat K$ vanishes outside $K$. The goal of this paper is to establish conditions on $K$ under which the support theorem holds for $K$.