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

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

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