[ספר][B] Geometric inverse problems

GP Paternain, M Salo, G Uhlmann - 2023‏ - books.google.com
This up-to-date treatment of recent developments in geometric inverse problems introduces
graduate students and researchers to an exciting area of research. With an emphasis on the …

Inverting the local geodesic X-ray transform on tensors

P Stefanov, G Uhlmann, A Vasy - Journal d'Analyse Mathematique, 2018‏ - Springer
We prove the local invertibility, up to potential fields, and stability of the geodesic X-ray
transform on tensor fields of order 1 and 2 near a strictly convex boundary point, on …

On an inverse boundary value problem for a nonlinear elastic wave equation

G Uhlmann, J Zhai - Journal de Mathématiques Pures et Appliquées, 2021‏ - Elsevier
We consider an inverse boundary value problem for a nonlinear elastic wave equation
which was studied in [1]. We show that all the parameters appearing in the equation can be …

Integral geometry on manifolds with boundary and applications

J Ilmavirta, F Monard - The Radon Transform: The First, 2019‏ - degruyter.com
4 Integral geometry on manifolds with boundary and applications Page 1 Joonas Ilmavirta
and François Monard 4 Integral geometry on manifolds with boundary and applications …

Lens rigidity for manifolds with hyperbolic trapped sets

C Guillarmou - Journal of the American Mathematical Society, 2017‏ - ams.org
For a Riemannian manifold $(M, g) $ with strictly convex boundary $\partial M $, the lens
data consist of the set of lengths of geodesics $\gamma $ with end points on $\partial M …

The geodesic X-ray transform with matrix weights

GP Paternain, M Salo, G Uhlmann… - American Journal of …, 2019‏ - muse.jhu.edu
Consider a compact Riemannian manifold of dimension $\geq 3$ with strictly convex
boundary, such that the manifold admits a strictly convex function. We show that the …

Travel time tomography

P Stefanov, G Uhlmann, A Vasy, H Zhou - Acta Mathematica Sinica …, 2019‏ - Springer
We survey some results on travel time tomography. The question is whether we can
determine the anisotropic index of refraction of a medium by measuring the travel times of …

Reconstruction and interpolation of manifolds. I: The geometric Whitney problem

C Fefferman, S Ivanov, Y Kurylev, M Lassas… - Foundations of …, 2020‏ - Springer
We study the geometric Whitney problem on how a Riemannian manifold (M, g) can be
constructed to approximate a metric space (X, d_X)(X, d X). This problem is closely related to …

A minicourse on microlocal analysis for wave propagation

A Vasy - Asymptotic analysis in general relativity, 2018‏ - books.google.com
This minicourse describes a microlocal framework for the linear analysis that has been
useful for the global understanding of wave propagation phenomena. While it is useful to …

Deep learning architectures for nonlinear operator functions and nonlinear inverse problems

MV de Hoop, M Lassas, CA Wong - Mathematical Statistics and Learning, 2022‏ - ems.press
We develop a theoretical analysis for special neural network architectures, termed operator
recurrent neural networks, for approximating nonlinear functions whose inputs are linear …