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# Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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# On solenoidal-injective and injective ray transforms of tensor fields on surfaces

Venkateswaran P. Krishnan
• Centre For Applicable Mathematics, Tata Institute of Fundamental Research, Post Bag No. 6503, GKVK Post Office, Sharada Nagar, Chikkabommasandra, Bangalore 560065, India
• Email
• Other articles by this author:
/ Rohit K. Mishra
/ François Monard
Published Online: 2019-01-30 | DOI: https://doi.org/10.1515/jiip-2018-0067

## Abstract

We first give a constructive answer to the attenuated tensor tomography problem on simple surfaces. We then use this result to propose two approaches to produce vector-valued integral transforms, which are fully injective over tensor fields. The first approach is by construction of appropriate weights, which vary along the geodesic flow, generalizing the moment transforms. The second one is by changing the pairing with the tensor field to generate a collection of transverse ray transforms.

MSC 2010: 35R30; 35A22; 44A12

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Revised: 2018-11-27

Accepted: 2018-11-30

Published Online: 2019-01-30

Published in Print: 2019-08-01

Funding Source: National Science Foundation

Award identifier / Grant number: DMS-1616564

Award identifier / Grant number: DMS-1814104

V. P. Krishnan is partially supported by NSF grant DMS-1616564 and a SERB Matrics grant. F. Monard is partially funded by NSF grant DMS-1814104 and a Hellmann Fellowship.

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 27, Issue 4, Pages 527–538, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219,

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