Unique Continuation Results for Certain Generalized Ray Transforms of Symmetric Tensor Fields
Agrawal, D., Krishnan, V. P., & Sahoo, S. K. (2022). Unique Continuation Results for Certain Generalized Ray Transforms of Symmetric Tensor Fields. Journal of Geometric Analysis, 32(10), Article 245. https://doi.org/10.1007/s12220-022-00981-5
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Let Im denote the Euclidean ray transform acting on compactly supported symmetric m-tensor field distributions f, and I∗m be its formal L2 adjoint. We study a unique continuation result for the operator Nm=I∗mIm. More precisely, we show that if Nmf vanishes to infinite order at a point x0 and if the Saint-Venant operator W acting on f vanishes on an open set containing x0, then f is a potential tensor field. This generalizes two recent works of Ilmavirta and Mönkkönen who proved such unique continuation results for the ray transform of functions and vector fields/1-forms. One of the main contributions of this work is identifying the Saint-Venant operator acting on higher-order tensor fields as the right generalization of the exterior derivative operator acting on 1-forms, which makes unique continuation results for ray transforms of higher-order tensor fields possible. In the second half of the paper, we prove analogous unique continuation results for momentum ray and transverse ray transforms. ...
PublisherSpringer Science and Business Media LLC
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Related funder(s)Academy of Finland; European Commission
Funding program(s)Centre of Excellence, AoF
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about fundingS.K.S. was supported by Academy of Finland (Centre of Excellence in Inverse Modelling and Imaging, grant 284715) and European Research Council under Horizon 2020 (ERC CoG 770924).
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