MATH Seminar

Title: Weighted X-ray mapping properties on the Euclidean and Hyperbolic Disks
Seminar: Analysis and Differential Geometry
Speaker: Joey Zou of Northwestern University
Contact: Yiran Wang, yiran.wang@emory.edu
Date: 2023-09-29 at 11:00AM
Venue: Atwood 240
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Abstract: We discuss recent works studying the sharp mapping properties of weighted X-ray transforms and weighted normal operators. These include a C^\infty isomorphism result 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 also describe mapping properties for the weighted normal operator in terms of Sobolev-type spaces adapted to this distinguished differential operator. In addition, we discuss ongoing work which applies these results to the X-ray transform on the hyperbolic disk by using a projective equivalence between the Euclidean and hyperbolic disks. Joint works with N. Eptaminitakis, R. K. Mishra, and F. Monard.