A1 Journal article (refereed)
A sharp stability estimate for tensor tomography in non-positive curvature (2021)
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
JYU authors or editors
Publication details
All authors or editors: Paternain, Gabriel P.; Salo, Mikko
Journal or series: Mathematische Zeitschrift
ISSN: 0025-5874
eISSN: 1432-1823
Publication year: 2021
Publication date: 12/11/2020
Volume: 298
Issue number: 3-4
Pages range: 1323-1344
Publisher: Springer
Publication country: Germany
Publication language: English
DOI: https://doi.org/10.1007/s00209-020-02638-x
Publication open access: Openly available
Publication channel open access: Partially open access channel
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/72638
Web address of parallel published publication (pre-print): https://arxiv.org/abs/2001.04334
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.
Keywords: partial differential equations; inverse problems
Contributing organizations
Related projects
- Centre of Excellence in Inverse Modelling and Imaging
- Salo, Mikko
- Academy of Finland
- Inverse boundary problems: toward a unified theory
- Salo, Mikko
- Academy of Finland
- Inverse boundary problems - toward a unified theory
- Salo, Mikko
- European Commission
Ministry reporting: Yes
Reporting Year: 2021
JUFO rating: 2