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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- 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.
