反演Radon变换标准方法的一种额外可能性
An additional possibilities of the standard method of inverting the Radon transform
- Sobolev Institute of Mathematics（索博列夫数学研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对有限维欧几里得空间中Radon变换反演问题，指出现有公式仅适用于可微函数，提出通过修改光滑函数的证明来获得不连续函数情形的反演公式。
AI中文摘要：
本文考虑有限维欧几里得空间中Radon积分变换的反演问题。指出了该课题对于探测问题（probing issues）的相关性。注意到对于后一方向，自然应将被积函数视为不连续函数。然而，现有的反演公式仅对可微函数得到证明。因此，便产生了为不连续函数获取公式的问题。文中确定，所需结果可通过将现有针对光滑函数的证明进行某种修改而获得。
英文摘要：
The problem of inverting the Radon integral transform in finite-dimensional Euclidean space is considered. The relevance of this topic for probing issues is indicated. It is noted that for the latter direction, it is natural to consider the integrand as discontinuous function. However, the available inversion formulas are only proven for differentiable functions. Therefore, the question of obtaining formulas for discontinuous functions arises. It is set that the required results can be obtained by some modification of available proofs for smooth functions.
