Journal article
Support theorems for the transverse ray transform of tensor fields of rank m
Journal of mathematical analysis and applications, v 485(2), 123828
15 May 2020
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Abstract
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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Details
- Title
- Support theorems for the transverse ray transform of tensor fields of rank m
- Creators
- Anuj Abhishek - Drexel University
- Publication Details
- Journal of mathematical analysis and applications, v 485(2), 123828
- Publisher
- Elsevier
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000511493200026
- Scopus ID
- 2-s2.0-85077734744
- Other Identifier
- 991019168984204721
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- Web of Science research areas
- Mathematics
- Mathematics, Applied