Support Theorems and an Injectivity Result for Integral Moments of a Symmetric m-Tensor Field
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Publication:6285245
DOI10.1007/S00041-018-09649-7arXiv1704.02010WikidataQ123027288 ScholiaQ123027288MaRDI QIDQ6285245
Rohit Kumar Mishra, Anuj Abhishek
Publication date: 6 April 2017
Abstract: In this work, we show an injectivity result and support theorems for integral moments of a m-tensor field on a simple, real analytic, Riemannian manifold. Integral moments of m-tensor field were first introduced by Sharafutdinov. At first we generalize a Helgason type support theorem proven by Krishnan and Stefanov in "A support theorem for the geodesic ray transform of symmetric tensor fields", Inverse Problems and Imaging, 3(3):453-464,2009. We use this extended result along with the first m+1-integral moments of a m-tensor field to prove the aforementioned results.
Integral operators (47G10) Pseudodifferential operators (47G30) Methods of local Riemannian geometry (53B21)
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