SUPPORT THEOREMS FOR RADON TRANSFORMS ON REAL ANALYTIC LINE COMPLEXES IN 3-SPACE

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 R3 . Let f be a distribution of compact support on R3. Assume Y is a real analytic admissible line complex and Y0 is an open connected subset of Y with one line in Y0 disjoint from supp f . Under weak geometric assumptions, if the Radon transform of f is zero for all lines in Y0, then supp f intersects no line in Y0. 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.