We discuss recent works studying sharp mapping properties of weighted X-ray transforms on the Euclidean disk and hyperbolic disk. These include a C^\infty isomorphism result (joint with R. Mishra and F. Monard) for certain weighted normal operators on the Euclidean disk, whose proof involves studying the spectrum of a distinguished Keldysh-type degenerate elliptic differential operator. We then discuss how to transfer these results to the hyperbolic disk (joint with N. Eptaminitakis and F. Monard), by using a projective equivalence between the Euclidean and hyperbolic disks via the Beltrami-Klein model.

https://sites.uci.edu/inverse/

https://sites.uci.edu/inverse/

https://sites.uci.edu/inverse/

https://sites.uci.edu/inverse/