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A hypersurface containing the support of a Radon transform must be an ellipsoid. II: The general case
Journal of Inverse and Ill-posed Problems ( IF 0.9 ) Pub Date : 2021-06-01 , DOI: 10.1515/jiip-2020-0139
Jan Boman 1
Affiliation  

If the Radon transform of a compactly supported distribution f≠0{f\neq 0} in ℝn{\mathbb{R}^{n}} is supported on the set of tangent planes to the boundary ∂⁡D{\partial D} of a bounded convex domain D , then ∂⁡D{\partial D} must be an ellipsoid. The special case of this result when the domain D is symmetric was treated in [J. Boman, A hypersurface containing the support of a Radon transform must be an ellipsoid. I: The symmetric case, J. Geom. Anal. 2020, 10.1007/s12220-020-00372-8]. Here we treat the general case.

中文翻译:

包含 Radon 变换支持的超曲面必须是椭球体。二:一般情况

如果紧支持分布 f≠0{f\neq 0} 在 ℝn{\mathbb{R}^{n}} 中的 Radon 变换在边界 ∂⁡D{\partial D} 的切平面集上得到支持的有界凸域 D ,则∂⁡D{\partial D} 必须是椭球。当域 D 是对称的时,这个结果的特殊情况在 [J. Boman,包含支持 Radon 变换的超曲面必须是椭球体。I:对称情况,J. Geom。肛门。2020,10.1007/s12220-020-00372-8]。这里我们处理一般情况。
更新日期:2021-06-01
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