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

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 R 3 . Let f be a distribution of compact support on 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