Support theorem for the Light-Ray transform of vector fields on Minkowski spaces

We study the Light-Ray transform of integrating vector fields on the Minkowski time-space $\boldsymbol{{\rm R}}^{1+n}$, $n≥ 2$, with the Minkowski metric. We prove a support theorem for vector fields vanishing on an open set of light-like lines. We provide examples to illustrate the application of our results to the inverse problem for the hyperbolic Dirichlet-to-Neumann map.

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