Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.09611 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908587175968768 |
|---|---|
| author | Gupta, Pranav Novikov, Roman |
| author_facet | Gupta, Pranav Novikov, Roman |
| contents | We define a discrete version of the non-abelian X-ray transform, going back in particular to Manakov, Zakharov (1981) and Strichartz (1982). We extend to this transform non-overdetermined reconstruction results obtained for the abelian case in the recent article by Novikov, Sharma (2025). In addition, we establish relations with the continuous non-abelian X-ray transform. In this respect, our results include an explicit and exact non-overdetermined layer-stripping reconstruction procedure for piecewise constant matrix-valued functions from their continuous non-abelian X-ray transform. To our knowledge, this result is new even for the classical X-ray transform. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09611 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discrete non-abelian X-ray transforms Gupta, Pranav Novikov, Roman Functional Analysis Mathematical Physics 44A12, 65R10, 65N21, 65N22 We define a discrete version of the non-abelian X-ray transform, going back in particular to Manakov, Zakharov (1981) and Strichartz (1982). We extend to this transform non-overdetermined reconstruction results obtained for the abelian case in the recent article by Novikov, Sharma (2025). In addition, we establish relations with the continuous non-abelian X-ray transform. In this respect, our results include an explicit and exact non-overdetermined layer-stripping reconstruction procedure for piecewise constant matrix-valued functions from their continuous non-abelian X-ray transform. To our knowledge, this result is new even for the classical X-ray transform. |
| title | Discrete non-abelian X-ray transforms |
| topic | Functional Analysis Mathematical Physics 44A12, 65R10, 65N21, 65N22 |
| url | https://arxiv.org/abs/2510.09611 |