Normal operators for momentum ray transforms, II: Saint Venant operators Full article
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Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304 |
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| Output data | Year: 2025, Volume: 21, Number: 1, Pages: 650-661 Pages count : 12 DOI: 10.33048/semi.2025.22.042 | ||||||
| Tags | ray transform, inverse problems, Saint-Venant operator, tensor tomography, momentum ray transform | ||||||
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0006 |
Abstract:
The momentum ray transform Ik m integrates a rank m symmetric tensor eld f on Rn over lines with the weight tk, Ik mf(x,ξ) = ∞ −∞ tk⟨f(x + tξ),ξm⟩dt. Let Nk m = (Ik m)∗Ik m be the normal operator of Ik m. To what extent is a symmetric m-tensor eld f determined by the data (N0 mf,...,Nr mf) for some 0 ≤ r ≤ m? The Saint Venant operator Wr m is a linear di erential operator of order m−r with constant coe cients on the space of symmetric m-tensor elds. We derive an explicit formula expressing Wr mf in terms of (N0 mf,...,Nr mf). The tensor eld Wr mf represents the full local information on f that can be extracted from the data (N0 mf,...,Nr mf)
Cite:
Jathar S.R.
, Kar M.
, Krishnan V.P.
, Shatafutdinov V.A.
Normal operators for momentum ray transforms, II: Saint Venant operators
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2025. V.21. N1. P.650-661. DOI: 10.33048/semi.2025.22.042
Normal operators for momentum ray transforms, II: Saint Venant operators
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2025. V.21. N1. P.650-661. DOI: 10.33048/semi.2025.22.042
Dates:
| Submitted: | Aug 21, 2024 |
| Published print: | Jul 4, 2025 |
| Published online: | Jul 4, 2025 |
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