The Geodesic Ray Transform on Spherically Symmetric Reversible Finsler Manifolds
Abstract
We show that the geodesic ray transform is injective on scalar functions on spherically symmetric reversible Finsler manifolds where the Finsler norm satisfies a Herglotz condition. We use angular Fourier series to reduce the injectivity problem to the invertibility of generalized Abel transforms and by Taylor expansions of geodesics we show that these Abel transforms are injective. Our result has applications in linearized boundary rigidity problem on Finsler manifolds and especially in linearized elastic travel time tomography.
Main Authors
Format
Articles
Research article
Published
2023
Series
Subjects
Publication in research information system
Publisher
Springer Science and Business Media LLC
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202303062015Use this for linking
Review status
Peer reviewed
ISSN
1050-6926
DOI
https://doi.org/10.1007/s12220-022-01182-w
Language
English
Published in
Journal of Geometric Analysis
Citation
- Ilmavirta, J., & Mönkkönen, K. (2023). The Geodesic Ray Transform on Spherically Symmetric Reversible Finsler Manifolds. Journal of Geometric Analysis, 33(4), Article 137. https://doi.org/10.1007/s12220-022-01182-w
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Funder(s)
Research Council of Finland
Research Council of Finland
Research Council of Finland
Research Council of Finland
Funding program(s)
Academy Research Fellow, AoF
Research costs of Academy Research Fellow, AoF
Centre of Excellence, AoF
Academy Project, AoF
Akatemiatutkija, SA
Akatemiatutkijan tutkimuskulut, SA
Huippuyksikkörahoitus, SA
Akatemiahanke, SA
Additional information about funding
J.I. was supported by Academy of Finland (Grants 332890, 336254, 351665, 351656). K.M. was supported by Academy of Finland (Center of Excellence in Inverse Modeling and Imaging, Grant Numbers 284715 and 309963). We wish to thank the anonymous referee for feedback.
Open Access funding provided by University of Jyväskylä (JYU).
Copyright© The Author(s) 2023