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PreprintarXiv licencearXiv

(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 tα for any α∈(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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Cite

BibTeXRIS
BibTeX
@misc{busch2026instability,
  title = {{(In)stability results for the Light Ray Transform}},
  author = {Leonard Busch and Sebastián Muñoz-Thon and Lauri Oksanen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14387},
  eprint = {2609.14387},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14387},
}
RIS
TY  - UNPB
TI  - (In)stability results for the Light Ray Transform
AU  - Leonard Busch
AU  - Sebastián Muñoz-Thon
AU  - Lauri Oksanen
PY  - 2026
DA  - 2026/09/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.14387
UR  - https://arxiv.org/abs/2609.14387
AB  - 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∈(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.
ER  -