Opuscula Math. 36, no. 2 (2016), 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.

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• Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A.
• Communicated by Semyon B. Yakubovich.
• Revised: 2015-09-18.
• Accepted: 2015-10-11.
• Published online: 2015-12-18.