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  • Functional Relations, Sharp Mapping Properties, and Regularization of the X-Ray Transform on Disks of Constant Curvature
Title: Functional Relations, Sharp Mapping Properties, and Regularization of the X-Ray Transform on Disks of Constant Curvature
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.  more » « less
Award ID(s):
1814104
PAR ID:
10468492
Author(s) / Creator(s):
Publisher / Repository:
SIAM
Date Published:
Journal Name:
SIAM Journal on Mathematical Analysis
Volume:
52
Issue:
6
ISSN:
0036-1410
Page Range / eLocation ID:
5675 to 5702
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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