A sharp stability estimate for tensor tomography in non-positive curvature
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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Mathematische ZeitschriftDate
2021Discipline
Inversio-ongelmien huippuyksikköMatematiikkaCentre of Excellence in Inverse ProblemsMathematicsCopyright
© The Author(s) 2020
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.
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https://converis.jyu.fi/converis/portal/detail/Publication/47012953
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Research Council of Finland; European CommissionFunding program(s)
Centre of Excellence, AoF; ERC Consolidator Grant; Academy Project, AoF
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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 Coun ...
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