21 citations · 67 across the 9 of their papers we have counts for
9 papers
Numerical approximation of the potential in the two-dimensional inverse scattering problem
Juan Antonio Barceló, Carlos Castro, Juan Manuel Reyes
We present an iterative algorithm to compute numerical approximations of the potential for the Schrödinger operator from scattering data. Four different types of scattering data ar…
A Hybrid Segmentation and D-bar Method for Electrical Impedance Tomography
Sarah Hamilton, Juan Manuel Reyes, Samuli Siltanen +1
The Regularized D-bar method for Electrical Impedance Tomography provides a rigorous mathematical approach for solving the full nonlinear inverse problem directly, i.e. without ite…
Uniqueness for an inverse problem in electromagnetism with partial data
Malcolm Brown, Marco Marletta, Juan Manuel Reyes
A uniqueness result for the recovery of the electric and magnetic coefficients in the time-harmonic Maxwell equations from local boundary measurements is proven. No special geometr…
Nonlinear Fourier analysis for discontinuous conductivities: computational results
Kari Astala, Lassi Päivärinta, Juan Manuel Reyes +1
Two reconstruction methods of Electrical Impedance Tomography (EIT) are numerically compared for nonsmooth conductivities in the plane based on the use of complex geometrical optic…
Inverse backscattering for the Schrödinger equation in 2D
Juan Manuel Reyes
We study the inverse backscattering problem for the Schrödinger equation in two dimensions. We prove that, for a non-smooth potential in 2D the main singularities up to 1/2 of the…
Stability of the Calderón problem for less regular conductivities
Pedro Caro, Andoni García, Juan Manuel Reyes
In these notes we prove log-type stability for the Calderón problem with conductivities in . We follow the lines of a recent work by Haberman and Tataru…
Mean convergence of Fourier-Dunkl series
Ó. Ciaurri, M. Pérez, J. M. Reyes +1
In the context of the Dunkl transform a complete orthogonal system arises in a very natural way. This paper studies the weighted norm convergence of the Fourier series expansion as…
Reconstruction of the singularities of a potential from backscattering data in 2D and 3D
Juan Manuel Reyes, Alberto Ruiz
We prove that the singularities of a potential in the two and three dimensional Schrödinger equation are the same as the singularities of the Born approximation (Diffraction Tomogr…
A Gaussian Weave for Kinematical Loop Quantum Gravity
A. Corichi, J. M. Reyes
Remarkable efforts in the study of the semi-classical regime of kinematical loop quantum gravity are currently underway. In this note, we construct a ``quasi-coherent'' weave state…