Functional relations, sharp mapping properties and regularization of the X-ray transform on disks of constant curvature

François Monard

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arXiv · 1910.13691

Functional relations, sharp mapping properties and regularization of the X-ray transform on disks of constant curvature

François Monard

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Abstract

On simple geodesic disks of constant curvature, we derive new functional relations for the geodesic X-ray transform, involving a certain class of elliptic differential operators whose ellipticity degenerates normally at the boundary. We then use these relations to derive sharp mapping properties for the X-ray transform and its corresponding normal operator. Finally, we discuss the possibility of theoretically rigorous regularized inversions for the X-ray transform when defined on such manifolds.

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François Monard. 2019-10-30. Functional relations, sharp mapping properties and regularization of the X-ray transform on disks of constant curvature. https://arxiv.org/abs/1910.13691

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