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The Geodesic Ray Transform on Spherically Symmetric Reversible Finsler Manifolds
Ilmavirta, Joonas; Mönkkönen, Keijo (Springer Science and Business Media LLC, 2023)We show that the geodesic ray transform is injective on scalar functions on spherically symmetric reversible Finsler manifolds where the Finsler norm satisfies a Herglotz condition. We use angular Fourier series to reduce ... -
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 ... -
Tensor Tomography on Negatively Curved Manifolds of Low Regularity
Ilmavirta, Joonas; Kykkänen, Antti (Springer, 2024)We prove solenoidal injectivity for the geodesic X-ray transform of tensor fields on simple Riemannian manifolds with C1,1 metrics and non-positive sectional curvature. The proof of the result rests on Pestov energy estimates ... -
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 ... -
Stable reconstruction of simple Riemannian manifolds from unknown interior sources
de Hoop, Maarten V.; Ilmavirta, Joonas; Lassas, Matti; Saksala, Teemu (IOP Publishing, 2023)Consider the geometric inverse problem: there is a set of delta-sources in spacetime that emit waves travelling at unit speed. If we know all the arrival times at the boundary cylinder of the spacetime, can we reconstruct ...