A support theorem for the Radon transform in the complex plane
type: Item
instance of: scholarly article
title: A support theorem for the Radon transform in the complex plane
zbMATH Open document ID: 0852.44002
DOI: 10.1007/BF01209564
author: A. B. Sekerin
published in: Mathematical Notes
publication date: 1994-11-16T00:00:00Z
review text: 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 \(\{z\mid \langle z,w_0 \rangle= s_0\}\).
Mathematics Subject Classification ID: 44A12
zbMATH DE Number: 687513
zbMATH Keywords: support theorem
zbMATH Keywords: complex plane
zbMATH Keywords: complex Radon transform
MaRDI profile type: Publication
cites work: The Radon transform
cites work: Uniform asymptotic expansions at a caustic
cites work: Support theorems for real-analytic Radon transforms
cites work: Q3682984
description: scientific article; zbMATH DE number 687513