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April  2018, 12(2): 293-314. doi: 10.3934/ipi.2018013

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

 Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA

Received  October 2016 Revised  December 2017 Published  February 2018

Fund Project: Partly supported by NSF Grants DMS 1301646 and DMS 1600327.

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.

Citation: Siamak RabieniaHaratbar. Support theorem for the Light-Ray transform of vector fields on Minkowski spaces. Inverse Problems & Imaging, 2018, 12 (2) : 293-314. doi: 10.3934/ipi.2018013
##### References:

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##### References:
$\Gamma_{\rho_0}$ with $0 <c < 1$.
$\Gamma_{0}$ with $0 <c <1$.
$\Gamma_{0}$ with $0 <c < 1$.
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