The Light ray transform for pseudo-Euclidean metrics

Abstract

We study the ray transform $L$ over null (light) rays in the pseudo-Euclidean space with signature $(n^{\prime },n^{\prime \prime })$, $n^{\prime }\ge 2$, $n^{\prime \prime }\ge 2$. We analyze the normal operator $L^{\prime }L$, derive an inversion formula, and prove stability estimates. We show that the symbol $p(\hat{I}¾)$ 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.