Microlocal analysis of the light ray transform on globally hyperbolic Lorentzian manifolds

Yiran Wang

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arXiv · 2104.08576

Microlocal analysis of the light ray transform on globally hyperbolic Lorentzian manifolds

Yiran Wang

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Abstract

For the light ray transform on globally hyperbolic Lorentzian manifolds of dimension $n+1 \geq 3$ acting on compactly supported distributions, we show that the Schwartz kernel of the normal operator is a paired Lagrangian distribution with non-vanishing principal symbols on each Lagrangians. We obtain Sobolev estimates for the light ray transform, and clarify the determination of light-like singularities using the normal operator.

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Yiran Wang. 2021-04-17. Microlocal analysis of the light ray transform on globally hyperbolic Lorentzian manifolds. https://arxiv.org/abs/2104.08576

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