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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Support theorems for Radon transforms on real analytic line complexes in three-space


Authors: Jan Boman and Eric Todd Quinto
Journal: Trans. Amer. Math. Soc. 335 (1993), 877-890
MSC: Primary 58G15; Secondary 44A12, 58G07
MathSciNet review: 1080733
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Abstract: In this article we prove support theorems for Radon transforms with arbitrary nonzero real analytic measures on line complexes (three-dimensional sets of lines) in $ {\mathbb{R}^3}$. Let $ f$ be a distribution of compact support on $ {\mathbb{R}^3}$. Assume $ Y$ is a real analytic admissible line complex and $ {Y_0}$ is an open connected subset of $ Y$ with one line in $ {Y_0}$ disjoint from supp$ \;f$. Under weak geometric assumptions, if the Radon transform of $ f$ is zero for all lines in $ {Y_0}$, then supp$ \;f$ intersects no line in $ {Y_0}$. These theorems are more general than previous results, even for the classical transform. We also prove a support theorem for the Radon transform on a nonadmissible line complex. Our proofs use analytic microlocal analysis and information about the analytic wave front set of a distribution at the boundary of its support.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1080733-8
PII: S 0002-9947(1993)1080733-8
Keywords: Radon transform, admissible line complex, analytic microlocal analysis
Article copyright: © Copyright 1993 American Mathematical Society