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

Range characterization of ray transform on Sobolev spaces of symmetric tensor fields Full article

Journal

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

Output data

Year: 2024, Volume: 18, Number: 6, Pages: 1272-1293 Pages count : 22 DOI: 10.3934/ipi.2024014

Funding (1)

Sobolev Institute of Mathematics

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

Submitted:	Jan 15, 2024
Published online:	Mar 29, 2024
Published print:	Dec 16, 2024

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

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