A support theorem for the Radon transform in the complex plane
Let \(\varphi (z)\in C_\mathbb{C} (\mathbb{C}^n)\). Let \(\widehat {\varphi} (s, w)\) be the complex Radon transform of \(\varphi\). Assume that the point \((s_0, w_0)\) does not belong to the support of \(\widehat {\varphi}\). Assume further that there exists an open connected unbounded set \(M\subset \mathbb{C}\) such that \(s_0\in M\) and the intersection \((M\times \{w_0\}) \cap \text{Supp } \widehat {\varphi}\) is empty. Then the function \(\varphi\) is equal to zero on the hyperplane \(\{z\mid \langle z,w_0 \rangle= s_0\}\).
scientific article; zbMATH DE number 687513