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Support theorems for the transverse ray transform of tensor fields of rank m
Journal article   Open access   Peer reviewed

Support theorems for the transverse ray transform of tensor fields of rank m

Anuj Abhishek
Journal of mathematical analysis and applications, v 485(2), 123828
15 May 2020
url
https://doi.org/10.1016/j.jmaa.2019.123828View
Published, Version of Record (VoR)Open Access (Publisher-Specific) Open

Abstract

Analytic microlocal analysis Support theorem Transverse ray transform
Let m and n be integers satisfying m≥2 and n≥m+2. Let (M,g) be a simple, real analytic, Riemannian manifold of dimension n with boundary and f be a rank m-tensor field defined over it. In this work, we prove a support theorem for the transverse ray transform of such tensor fields. More specifically, we prove that for a tensor field f of rank m, if the transverse ray transform of f vanishes over an appropriate open set of maximal geodesics of M, then the support of f vanishes on the points of M that lie on the union of the aforementioned open set of geodesics. We also show that if the tensor field is assumed to be symmetric, then one has a similar support theorem for the transverse ray transform of symmetric tensor fields of rank up to n−1.

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Web of Science research areas
Mathematics
Mathematics, Applied
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