Pestov identities and X-ray tomography on manifolds of low regularity
Ilmavirta, J., & Kykkänen, A. (2023). Pestov identities and X-ray tomography on manifolds of low regularity. Inverse Problems and Imaging, Early Access. https://doi.org/10.3934/ipi.2023017
Julkaistu sarjassa
Inverse Problems and ImagingPäivämäärä
2023Tekijänoikeudet
© 2023 American Institute of Mathematical Sciences (AIMS)
We prove that the geodesic X-ray transform is injective on scalar functions and (solenoidally) on one-forms on simple Riemannian manifolds (M, g) with g ∈ C1,1. In addition to a proof, we produce a redefinition of simplicity that is compatible with rough geometry. This C1,1-regularity is optimal on the Hölder scale. The bulk of the article is devoted to setting up a calculus of differential and curvature operators on the unit sphere bundle atop this non-smooth structure.
Julkaisija
American Institute of Mathematical Sciences (AIMS)ISSN Hae Julkaisufoorumista
1930-8337Asiasanat
Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/182855192
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Suomen AkatemiaRahoitusohjelmat(t)
Akatemiatutkija, SA![](/themes/JYX2/images/funders/sa_logo_thumb.jpg)
Lisätietoja rahoituksesta
Both authors were supported by the Academy of Finland (JI by grants 332890 and 351665, AK by 336254).Lisenssi
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Pestov identities and X-ray tomography on manifolds of low regularity
Ilmavirta, Joonas; Kykkänen, Antti (American Institute of Mathematical Sciences (AIMS), 2023)We prove that the geodesic X-ray transform is injective on scalar functions and (solenoidally) on one-forms on simple Riemannian manifolds (M, g) with g ∈ C1,1. In addition to a proof, we produce a redefinition of simplicity ... -
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