With the proofs of the range characterization and support theorems for the radon transform complete, let’s take a step back and look at the intuition behind these results again. In particular, let’s try to understand the moment conditions (It might be good to read this post *before* reading the full proofs). It was easy to directly verify that the moment conditions were necessary, so

We need to show it is sufficient — that . Take $g \ in \mathcal{S}_H(\mathbb{R}\times S^{n-1})$, we need to find with Continue reading