The Light ray transform for pseudo-Euclidean metrics

2025/02/19 by Agrawal, Divyansh, Stefanov, Plamen · 1 citation
#35R30 #44A12 #53C65 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.13684

Abstract

We study the ray transform L over null (light) rays in the pseudo-Euclidean space with signature (n',n''), n'≥2, n''≥2. We analyze the normal operator L'L, derive an inversion formula, and prove stability estimates. We show that the symbol p(ξ) is elliptic but singular at the light cone. We analyze L as an Fourier Integral Operator as well. Finally, we compare this to the Minkowski case.

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