EVENT DETAILS AND ABSTRACT

Title: Sharp Mapping Properties for Weighted X-ray Transforms and Self-adjoint Realizations of Degenerately Elliptic Operators
Speaker: Joey Zou
Speaker Info: Northwestern
Brief Description:
Special Note:
Abstract:

I will present joint work with R. Mishra and F. Monard regarding mapping properties (especially regarding behavior up to the boundary) of singularly-weighted normal operators associated to X-ray transforms on manifolds with boundary. The proof involves deriving the Singular Value Decomposition of a weighted X-ray transform and studying certain function spaces based on the singular vectors of the X-ray transform, which coincides with the eigenfunctions of a particular degenerately elliptic Kimura-type differential operator. Time permitting, I will discuss ongoing work with F. Monard in studying the possible self-adjoint realizations of the degenerately elliptic operator in question.