Unique continuation for the momentum ray transform

TL;DR

This paper establishes unique continuation properties for weighted momentum ray transforms and cone transforms, leveraging the fractional Laplace operator's UCP, and introduces new conservative and antilocality properties for these transforms.

Contribution

It presents novel unique continuation results for momentum ray and cone transforms, expanding understanding of their conservative and antilocality properties using fractional Laplacian techniques.

Findings

Proves conservative property for momentum ray transforms on tensors.

Establishes antilocality for weighted ray and cone transforms on functions.

Utilizes the UCP of the fractional Laplace operator in the proofs.

Abstract

The present article focuses on a unique continuation result for certain weighted ray transforms, utilizing the unique continuation property (UCP) of the fractional Laplace operator. Specifically, we demonstrate a conservative property for momentum ray transforms acting on tensors, as well as the antilocality property for both weighted ray and cone transforms acting on functions.