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Applications of Microlocal Analysis in Inverse Problems
Salo, Mikko (MDPI AG, 2020)This note reviews certain classical applications of microlocal analysis in inverse problems. The text is based on lecture notes for a postgraduate level minicourse on applications of microlocal analysis in inverse problems, ... -
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 ... -
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 ...