The anisotropic Calderón problem at large fixed frequency on manifolds with invertible ray transform
Abstract
We consider the inverse problem of recovering a potential from the Dirichlet to Neumann map at a large fixed frequency on certain Riemannian manifolds. We extend the earlier result of Uhlmann and Wang [arXiv:2104.03477] to the case of simple manifolds, and more generally to manifolds where the geodesic ray transform is stably invertible. The argument involves an invariantly formulated construction of Gaussian beam quasimodes with uniform bounds for the underlying constants.
Main Authors
Format
Articles
Research article
Published
2024
Series
Subjects
Publication in research information system
Publisher
Wiley
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202410216418Use this for linking
Review status
Peer reviewed
ISSN
0024-6107
DOI
https://doi.org/10.1112/jlms.13006
Language
English
Published in
Journal of the London Mathematical Society
Citation
- Ma, S., Sahoo, S. K., & Salo, M. (2024). The anisotropic Calderón problem at large fixed frequency on manifolds with invertible ray transform. Journal of the London Mathematical Society, 110(4), Article e13006. https://doi.org/10.1112/jlms.13006
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Funder(s)
Research Council of Finland
European Commission
Funding program(s)
Centre of Excellence, AoF
ERC Consolidator Grant
Huippuyksikkörahoitus, SA
ERC Consolidator Grant
Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Education and Culture Executive Agency (EACEA). Neither the European Union nor EACEA can be held responsible for them.
Additional information about funding
All the authors were partly supported by the Academy of Finland (Centre of Excellence in Inverse Modelling and Imaging, grant 284715) and by the European Research Council under Horizon 2020 (ERC CoG 770924). The research of S. Ma is partially supported by the NSF of China under the grant no. 12301540.
Copyright© 2024 The Author(s). Journal of the London Mathematical Society is copyright © London Mathematical Society.