A sharp stability estimate for tensor tomography in non-positive curvature
Abstract
We consider the geodesic X-ray transform acting on solenoidal tensor fields on a compact simply connected manifold with strictly convex boundary and non-positive curvature. We establish a stability estimate of the form L2↦H1/2TL2↦HT1/2, where the H1/2THT1/2-space is defined using the natural parametrization of geodesics as initial boundary points and incoming directions (fan-beam geometry); only tangential derivatives at the boundary are used. The proof is based on the Pestov identity with boundary term localized in frequency.
Main Authors
Format
Articles
Research article
Published
2021
Series
Subjects
Publication in research information system
Publisher
Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202011176658Use this for linking
Review status
Peer reviewed
ISSN
0025-5874
DOI
https://doi.org/10.1007/s00209-020-02638-x
Language
English
Published in
Mathematische Zeitschrift
Citation
- Paternain, G. P., & Salo, M. (2021). A sharp stability estimate for tensor tomography in non-positive curvature. Mathematische Zeitschrift, 298(3-4), 1323-1344. https://doi.org/10.1007/s00209-020-02638-x
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Funder(s)
Research Council of Finland
European Commission
Research Council of Finland
Funding program(s)
Centre of Excellence, AoF
ERC Consolidator Grant
Academy Project, AoF
Huippuyksikkörahoitus, SA
ERC Consolidator Grant
Akatemiahanke, SA
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
We are very grateful to the referee for several comments that improved the presentation and in particular for suggesting a simplified proof of Lemma 4.4. GPP was supported by EPSRC Grant EP/R001898/1 and the Leverhulme trust. MS was supported by the Academy of Finland (Finnish Centre of Excellence in Inverse Modelling and Imaging, Grant Numbers 312121 and 309963) and by the European Research Council under Horizon 2020 (ERC CoG 770924). This material is based upon work supported by the National Science Foundation under Grant No. 1440140, while the authors were in residence at MSRI in Berkeley, California, during the semester on Microlocal Analysis in 2019.
Copyright© The Author(s) 2020