| Abstract: |
| The overarching theme of this talk is concerned with the mapping properties of X-ray transforms on manifolds with strictly convex boundary.
On certain symmetric manifolds with constant curvature and strictly convex boundary, recent functional relations between the X-ray transform and degenerate elliptic operators provide the framework to understand on what scales of spaces the X-ray transform satisfies tame estimates (i.e. finite-degree smoothing with finite-degree unsmoothing inverse) that holds all the way to the boundary. I will discuss these results, as well as recent results with Yuzhou Zou regarding a refined study of these degenerate elliptic operators.
Related recent works:
http://arxiv.org/abs/2112.14904
http://arxiv.org/abs/2203.09861
http://arxiv.org/abs/2302.08133 |
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