A two cones support theorem

Abstract

Abstract. We show that if the Radon transform of a distribution f vanishes outside of an acute cone C0, the support of the distribution is contained in the union of C0 and another acute cone C1, the cones are in a suitable position, and f vanishes distributionally in the direction of the axis of C1, then actually supp f ⊂ C0. We show by examples that this result is sharp.