Range characterization of ray transform on Sobolev spaces of symmetric tensor fields | Sciact - Система учета научной деятельности ИМ СО РАН

Range characterization of ray transform on Sobolev spaces of symmetric tensor fields Научная публикация

Журнал

Inverse Problems and Imaging
ISSN: 1930-8337 , E-ISSN: 1930-8345

Вых. Данные

Год: 2024, Том: 18, Номер: 6, Страницы: 1272-1293 Страниц : 22 DOI: 10.3934/ipi.2024014

Ключевые слова

Ray transform, Reshetnyak formula, range characterization, inverse problems, tensor analysis.

Авторы

Krishnan Venkateswaran P. ¹ , Sharafutdinov Vladimir A. ²

Организации

1	TIFR Centre for Applicable Mathematics
2	Sobolev Institute of Mathematics; 4 Koptyug Avenue, Novosibirsk, 630090, Russia

Информация о финансировании (1)

Институт математики им. С.Л. Соболева СО РАН

FWNF-2022-0006

The ray transform I integrates symmetric m-tensor field in Rn over lines. This transform on Sobolev spaces was studied in two earlier works of the second author where Reshetnyak formulas (isometry relations) and range characterization of ray transform of functions in dimensions n ≥ 3 were established. The main focus of the current work is range characterization of ray transform of symmetric tensor fields on Sobolev spaces generalizing the earlier result proved for the case of functions. In dimensions n ≥ 3, range characterization of the ray transform in Schwartz spaces is well-known; the main ingredient of the characterization is a system of linear differential equations of order 2(m+1) called John equations. Using zeroth order Reshetnyak formulas, the range of the ray transform on Sobolev spaces is characterized in dimensions n ≥3 in this paper.

Krishnan V.P. , Sharafutdinov V.A.
Range characterization of ray transform on Sobolev spaces of symmetric tensor fields
Inverse Problems and Imaging. 2024. V.18. N6. P.1272-1293. DOI: 10.3934/ipi.2024014 WOS Scopus OpenAlex

Поступила в редакцию:	15 янв. 2024 г.
Опубликована online:	29 мар. 2024 г.
Опубликована в печати:	16 дек. 2024 г.

Web of science:	WOS:001194354500001
Scopus:	2-s2.0-85202191512
OpenAlex:	W4393323366

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