RAY TRANSFORM ON SOBOLEV SPACES OF SYMMETRIC TENSOR FIELDS, I: HIGHER ORDER RESHETNYAK FORMULAS Научная публикация
| Журнал |
Inverse Problems and Imaging
ISSN: 1930-8337 , E-ISSN: 1930-8345 |
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| Вых. Данные | Год: 2022, Том: 16, Номер: 4, Страницы: 787-826 Страниц : 40 DOI: 10.3934/ipi.2021076 | ||||
| Ключевые слова | inverse problems; Ray transform; Reshetnyak formula; tensor analysis | ||||
| Авторы |
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| Организации |
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Информация о финансировании (1)
| 1 | Российский фонд фундаментальных исследований | 20-51-15004 |
Реферат:
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.
Библиографическая ссылка:
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
Даты:
| Поступила в редакцию: | 11 июн. 2021 г. |
| Принята к публикации: | 15 окт. 2021 г. |
| Опубликована online: | 15 дек. 2021 г. |
| Опубликована в печати: | 15 авг. 2022 г. |
Идентификаторы БД:
| Web of science: | WOS:000736357300001 |
| Scopus: | 2-s2.0-85133532282 |
| РИНЦ: | 49151474 |
| OpenAlex: | W3174171430 |