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.
Authors
- Suman Kumar Sahoo (ORCID: https://orcid.org/0000-0002-6459-1597)
- Mikko Salo (ORCID: https://orcid.org/0000-0002-3681-6779)
- Shiqi Ma (ORCID: https://orcid.org/0000-0002-0192-493X)
Institutions
- Indian Institute of Technology Bombay (IN)
- Jilin University (CN)
- University of Jyväskylä (FI)
Publication Details
- Journal
- Journal of the London Mathematical Society
- Published
- 2024-10-01
- DOI
- https://doi.org/10.1112/jlms.13006
- Citations
- 3
- Primary Topic
- Numerical methods in inverse problems
- Type
- article
- Field-Weighted Citation Impact
- 2.67
Funders
- National Science Foundation
- Isaac Newton Institute for Mathematical Sciences
- National Natural Science Foundation of China
- Engineering and Physical Sciences Research Council
- H2020 European Research Council