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

Ricardo Estrada

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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  • Ricardo Estrada
  • Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A.
  • Communicated by Semyon B. Yakubovich.
  • Received: 2015-07-03.
  • Revised: 2015-09-18.
  • Accepted: 2015-10-11.
  • Published online: 2015-12-18.
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Cite this article as:
Ricardo Estrada, A two cones support theorem, Opuscula Math. 36, no. 2 (2016), 207-213, http://dx.doi.org/10.7494/OpMath.2016.36.2.207

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