Opuscula Math. 36, no. 2 (), 207-213
http://dx.doi.org/10.7494/OpMath.2016.36.2.207
Opuscula Mathematica

# A two cones support theorem

Abstract. We show that if the Radon transform of a distribution $$f$$ vanishes outside of an acute cone $$C_{0}$$, the support of the distribution is contained in the union of $$C_{0}$$ and another acute cone $$C_{1}$$, the cones are in a suitable position, and $$f$$ vanishes distributionally in the direction of the axis of $$C_{1}$$, then actually $$\operatorname*{supp}f\subset C_{0}$$. We show by examples that this result is sharp.
Keywords: Radon transforms, support theorems, distributions.
Mathematics Subject Classification: 44A12, 46F10.