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arXiv · 2609.14387

(In)stability results for the Light Ray Transform

Leonard Busch·Sebastián Muñoz-Thon·Lauri Oksanen
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Abstract

We prove quantitative instability results for the light ray transform in the Minkowski setting, and locally in the smooth and Gevrey categories. In the smooth Sobolev setting, we show that no modulus of continuity can be better than $t^α$ for any $α\in(0,1)$, while in the Gevrey setting we obtain an explicit logarithmic lower bound. On the other hand, using the relation between stationary geometries and magnetic(-potential) systems, we obtain a stability result for "time moments" of the light ray transform.

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Leonard Busch, Sebastián Muñoz-Thon, Lauri Oksanen. 2026-09-13. (In)stability results for the Light Ray Transform. https://arxiv.org/abs/2609.14387

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