Showing items with similar title or keywords.

• X-ray Transforms in Pseudo-Riemannian Geometry 

  Ilmavirta, Joonas (Springer US, 2018)

  We study the problem of recovering a function on a pseudo-Riemannian manifold from its integrals over all null geodesics in three geometries: pseudo-Riemannian products of Riemannian manifolds, Minkowski spaces, and tori. ...

• On mixed and transverse ray transforms on orientable surfaces 

  Ilmavirta, Joonas; Mönkkönen, Keijo; Railo, Jesse (Walter de Gruyter GmbH, 2023)

  The geodesic ray transform, the mixed ray transform and the transverse ray transform of a tensor field on a surface can all be seen as what we call mixing ray transforms, compositions of the geodesic ray transform and an ...

• 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 ...

• Geodesic ray transform with matrix weights for piecewise constant functions 

  Ilmavirta, Joonas; Railo, Jesse (Suomalainen tiedeakatemia, 2020)

  We show injectivity of the geodesic X-ray transform on piecewise constant functions when the transform is weighted by a continuous matrix weight. The manifold is assumed to be compact and nontrapping of any dimension, and ...

• Unique Continuation Results for Certain Generalized Ray Transforms of Symmetric Tensor Fields 

  Agrawal, Divyansh; Krishnan, Venkateswaran P.; Sahoo, Suman Kumar (Springer Science and Business Media LLC, 2022)

  Let Im denote the Euclidean ray transform acting on compactly supported symmetric m-tensor field distributions f, and I∗m be its formal L2 adjoint. We study a unique continuation result for the operator Nm=I∗mIm. More ...