RAY TRANSFORM ON SOBOLEV SPACES OF SYMMETRIC TENSOR FIELDS, I: HIGHER ORDER RESHETNYAK FORMULAS Full article
| Journal |
Inverse Problems and Imaging
ISSN: 1930-8337 , E-ISSN: 1930-8345 |
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| Output data | Year: 2022, Volume: 16, Number: 4, Pages: 787-826 Pages count : 40 DOI: 10.3934/ipi.2021076 | ||||
| Tags | inverse problems; Ray transform; Reshetnyak formula; tensor analysis | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Russian Foundation for Basic Research | 20-51-15004 |
Abstract:
For an integer r ≥ 0, we prove the rth order Reshetnyak formula for the ray transform of rank m symmetric tensor fields on Rn. Roughly speaking, for a tensor field f, the order r refers to L2-integrability of higher order derivatives of the Fourier transform̂f over spheres centered at the origin. Certain differential operators A(m,r,l) (0 ≤ l ≤ r) on the sphere Sn−1 are main ingredients of the formula. The operators are defined by an algorithm that can be applied for any r although the volume of calculations grows fast with r. The algorithm is realized for small values of r and Reshetnyak formulas of orders 0, 1, 2 are presented in an explicit form.
Cite:
Krishnan V.P.
, Sharafutdinov V.A.
RAY TRANSFORM ON SOBOLEV SPACES OF SYMMETRIC TENSOR FIELDS, I: HIGHER ORDER RESHETNYAK FORMULAS
Inverse Problems and Imaging. 2022. V.16. N4. P.787-826. DOI: 10.3934/ipi.2021076 WOS Scopus РИНЦ OpenAlex
RAY TRANSFORM ON SOBOLEV SPACES OF SYMMETRIC TENSOR FIELDS, I: HIGHER ORDER RESHETNYAK FORMULAS
Inverse Problems and Imaging. 2022. V.16. N4. P.787-826. DOI: 10.3934/ipi.2021076 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jun 11, 2021 |
| Accepted: | Oct 15, 2021 |
| Published online: | Dec 15, 2021 |
| Published print: | Aug 15, 2022 |
Identifiers:
| Web of science: | WOS:000736357300001 |
| Scopus: | 2-s2.0-85133532282 |
| Elibrary: | 49151474 |
| OpenAlex: | W3174171430 |