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Mixed ray transform on simple $ 2$-dimensional Riemannian manifolds


Authors: Maarten V. de Hoop, Teemu Saksala and Jian Zhai
Journal: Proc. Amer. Math. Soc. 147 (2019), 4901-4913
MSC (2010): Primary 44A12, 53A35, 53C22, 58C99, 58J90
DOI: https://doi.org/10.1090/proc/14601
Published electronically: June 10, 2019
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Abstract: We characterize the kernel of the mixed ray transform on simple $ 2$-dimensional Riemannian manifolds, that is, on simple surfaces for tensors of any order.


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Additional Information

Maarten V. de Hoop
Affiliation: Simons Chair in Computational and Applied Mathematics and Earth Science, Rice University, Houston, Texas 77005
Email: mdehoop@rice.edu

Teemu Saksala
Affiliation: Department of Computational and Applied Mathematics, Rice University, Houston, Texas, 77005
Email: teemu.saksala@rice.edu

Jian Zhai
Affiliation: Institute for Advanced Study, The Hong Kong University of Science and Technology, Hong Kong, China

DOI: https://doi.org/10.1090/proc/14601
Received by editor(s): August 7, 2018
Received by editor(s) in revised form: February 2, 2019, February 21, 2019, and February 22, 2019
Published electronically: June 10, 2019
Additional Notes: The work of the first author was partially supported by the Simons Foundation under the MATH + X program, the National Science Foundation under grant DMS-1815143, and by members of the Geo-Mathematical Imaging Group at Rice University.
The second author was supported by the Simons Foundation under the MATH + X program.
The third author was supported by the Simons Foundation under the MATH + X program.
Communicated by: Michael Hitrik
Article copyright: © Copyright 2019 American Mathematical Society